Russian leader Vladimir Putin has said UN officials will be granted permission to visit and inspect the Zaporizhzhia nuclear complex.
The Kremlin made the announcement after a call between Putin and French President Emmanuel Macron.
It came after UN chief Antonio Guterres told the BBC that he is "concerned" about the situation at the plant.
He said military activity around Zaporizhzhia must end and urged Moscow to grant access to inspectors.
The site has been under Russian occupation since early March but Ukrainian technicians still operate it under Russian direction.
In a readout following the call between the French and Russian leaders, the Kremlin said Putin had agreed to provide UN investigators with "the necessary assistance" to access the site.
"Both leaders noted the importance" of sending the IAEA experts to the plant for an assessment of "the situation on the ground," the Kremlin said.
International Atomic Energy Agency (IAEA) director-general Rafael Grossi, head of the UN's nuclear watchdog, welcomed Putin's statement, and said he was willing to lead a visit to the plant himself.
"In this highly volatile and fragile situation, it is of vital importance that no new action is taken that could further endanger the safety and security of one of the world's largest nuclear power plants," Grossi said.
Ukrainian officials said Russia had turned the complex into an army base - deploying military equipment, weapons and about 500 troops who were using the site as a shield to attack towns across the Dnieper River.
And in recent weeks the area around the facility came under heavy artillery fire, with Kyiv and Moscow blaming each other for the attacks.
On Thursday, during a meeting with Guterres and Turkish leader Recep Tayyip Erdogan, Ukrainian President Volodymyr Zelensky criticised "deliberate" Russian attacks on the power plant.
Despite displaying some willingness to grant access to inspectors, Russian officials have flatly refused international demands to demilitarise the site.
The Russian foreign ministry's information and press department deputy director Ivan Nechayev said on Friday that such moves would leave the plant "even more vulnerable".
Meanwhile, Russia submitted a letter to the UN Security Council detailing the "provocations" that it accused Ukraine of plotting at the Zaporizhzhia nuclear power plant.
The Russian mission to the UN alleged that the Ukrainians wanted to cause "what they believe to be a minor accident", consisting of a radiation leak, which could see Russia accused of "nuclear terrorism".
The letter denied that Russian troops are storing weapons on site. It repeated an allegation that the Ukrainians have been shelling the plant.
How risky is stand-off over Zaporizhzhia?
The rhetoric surrounding Europe's biggest nuclear power plant - close to the front line in Ukraine - has become increasingly alarming, with international figures warning of the risk of a major accident.
However, head of the Centre for Doctoral Training in Nuclear Energy Futures, Mark Wenman, said he "wouldn't be too worried".
"Zaporizhzhia was built in the 1980s, which is relatively modern. It has a solid containment building. It's 1.75m [5.75ft] thick, of heavily reinforced concrete on a seismic bed [to withstand earthquakes]... and it takes a hell of a lot to breach that," Wenman said.
He rejected comparisons with either Chernobyl in 1986 or Fukushima in 2011. Chernobyl had serious design flaws, he explained, while at Fukushima the diesel generators were flooded, which he believed would not happen in Ukraine as the generators were inside the containment building.
Much of the anxiety has been about the plant coming under fire from artillery shells or rockets but that may not be the biggest risk. After 9/11, nuclear plants were tested for potential attacks involving large airliners and found to be largely safe.
A potentially more serious hazard could come if the power supply to the nuclear reactors and back-up generators was lost and led to a loss of coolant. With no electricity to power the pumps around the hot reactor core, the fuel would start to melt.
Head of Russia's nuclear protection corps Lieutenant General Igor Kirillov said the plant's support systems had already been damaged by shelling, and that kind of pump and generator failure could lead to the reactor core overheating and the plant's facilities being destroyed.
"That wouldn't be as serious as Chernobyl, but it could still lead to a release of radioactivity and that depends which way the wind's blowing," said Claire Corkhill, professor of nuclear material degradation at the University of Sheffield.
For her, the risk of something going wrong was genuine - and Russia would be just as much at risk as Central Europe.
The IAEA, warned of a "very real risk of nuclear disaster" and asked to be allowed access to the site as soon as possible. The UN secretary general called on Russia to pull its troops out and demilitarise the area with a "safe perimeter". Russia refused, arguing that would make the plant more vulnerable.
Ukraine's nuclear agency said three of the four power transmission lines linking the plant to Ukraine had already been damaged by rocket fire. If the last source of power was also broken, the agency believed nuclear fuel would begin melting "resulting in a release of radioactive substances to the environment", and diesel generators would not provide a long-term solution.
But chair of nuclear engineering at the University of Ljubljana in Slovenia, Professor Iztok Tiselj, believed the risk of a major radioactive incident was minimal as only two of the six reactors were currently operating.
"From the standpoint of European citizens there's no reason to worry," he said. The other four were in a state of cold shutdown, so the amount of power needed to cool the reactors was smaller.
At the heart of this crisis are the plant's original staff, working under Russian occupation and quite probably under a great deal of stress. They have complained of the plant coming under continuous attack but also warned the real threat of disaster would emerge if Russia shut the whole plant down, so it could disconnect the supply from Ukraine and reconnect it instead to Russian-occupied Crimea.
If something were to go wrong, they would need to be on top form, and one can imagine they were not, said Claire Corkhill.
IAEA head Rafael Grossi appealed for the staff to be left to carry out their duties "without threats or pressure".
A letter signed by dozens of employees at the plant on Thursday called on the international community to stop and think: "We can professionally control nuclear fission," it said, "but we are helpless in the face of people's irresponsibility and madness."
- BBC