The issue is deeply divisive among Ukraine's supporters, with the United States and Germany reluctant to permit Ukraine to strike over the border out of fear it could drag them closer to direct conflict with Moscow.

On Tuesday, President Vladimir Putin warned of "serious consequences" if Western countries allowed Ukraine to use their weapons to strike Russia.

The Kremlin has also gloated over the persisting differences in the West.

"We see that there is no consensus on this issue in the Western camp," Kremlin spokesman Dmitry Peskov told Russian daily Izvestia on Tuesday.

He slammed the "hotheads who are making absolutely irresponsible and provocative statements."

"But there are also those who ask themselves the question 'Is it necessary to escalate further?'"

- Discord -

On Monday, NATO chief Jens Stoltenberg urged Western powers to reconsider the restrictions as they were hampering Kyiv's ability to defend itself.

But Washington and other allies are reluctant, fearing a possible escalation could prompt Putin to use nuclear weapons.

"I think this is unfair," Ukrainian leader Volodymyr Zelensky said about western restrictions on use of their weapons.

French military historian Michel Goya said there is little past evidence suggesting that a country providing lethal aid would get dragged into a conflict.

Western weapons have already been used on several occasions against Russia's territory, most recently against the southern town of Krasnodar, several Western sources said.

Moscow, Goya said, had claimed that Crimea annexed from Ukraine in 2014 was "untouchable."

"The Ukrainians hit it with American weapons and nothing happened", the former French colonel told AFP.

- 'Limitations' -

The stakes are huge. Ukraine is struggling to hold back a Russian ground offensive in the Kharkiv region, where Moscow recently made its largest territorial gains in 18 months.

With Russia's war against Ukraine in its third year, Ukrainian soldiers are exhausted and outgunned.

"Ukraine complains that the limitations imposed by the allies make it easier for Russia to establish a strategic, operational and tactical advantage," James Everard, former NATO Deputy Supreme Allied Commander Europe, told AFP.

Military experts say it is hard for Ukraine to defend itself if it cannot hit military targets on the other side of the border.

"Ukraine has been striking behind enemy lines since the start of the full-scale war," said analyst Ivan Klyszcz of the Estonia-based International Centre for Defence and Security.

Such strikes are essential to wear down enemy forces, disrupt their supply and logistics chains and engage in counter-battery fire, he said.

The question now is "whether these strikes should also take place inside Russia," said Klyszcz.

"The reality is that Russia's nuclear sabre-rattling and conventional armed forces have deterred many Western decision-makers from decidedly helping Ukraine in its war of self-defence."

- 'Self-deterred by Russia' -

The Western response to the invasion has been driven by fears of escalation, with Kyiv's allies initially hesitating to supply long-range missiles, heavy tanks and fighter jets.

Many of the initial red lines have eventually been crossed, but a lot of time has been lost as Western leaders dither, military experts say.

"In retrospect, we realise that if they had given in from the outset, it would have been more effective," said Goya.

He pointed out that "international law authorises a country under attack to strike the aggressor country provided that it respects humanitarian law."

"Our leaders are mainly risk-averse and financially challenged, and so self-deterred by Russia," said Everard.

He added that restrictions on the use of weapon systems are made by each of Ukraine's allies, not NATO, which complicates the situation further.

"Unsurprisingly this produces an uneven set of freedoms and constraints that are difficult to interpret."

- 'Follow Macron's lead' -

Many Kyiv allies also remain uneasy about the prospect of sending Western troops to Ukraine.

In February, French President Emmanuel Macron sparked an uproar among NATO members when he refused to rule out dispatching troops to Ukraine.

But with Ukraine ceding ground, signs are multiplying that countries like Poland, the Czech Republic and the Baltic States are warming to the idea.

"Macron's breaking of the taboo on discussing Western deployments of troops inside Ukraine was a watershed moment in Russia's diminishing deterrence," said Klyszcz.

Many allies, he added, are now "cautiously hinting at the possibility of deploying some sort of on-the-ground presence in the form of trainers or technical assistance."

Keir Giles, a senior consulting fellow at Chatham House, wrote that more European leaders should "follow Macron's lead."

"Publicly ruling out a Western troop presence in Ukraine makes no sense, whether or not it's a realistic proposition for some NATO countries," he said.

"Just the possibility is one of the Kremlin's greatest fears."