* Ukraine says rebels brought tanks across Russian border
* Poroshenko tells Putin situation is "unacceptable"
* Russia to cut off gas to Kiev if no deal by Monday
Evidence that Russia is sending in weapons or assisting the rebels militarily would implicate Moscow in the uprising against Kiev's pro-Western leaders, making a mockery of its denials that it has played a role in weeks of fighting.
Interior Minister Arseny Avakov stopped short of directly accusing Russia of sending the tanks but made clear he held President Vladimir Putin responsible for failing to carry out a promise to tighten controls at the border.
In a sign of his concern, President Petro Poroshenko discussed the situation with his defence and security chiefs and then told Putin by phone that the situation was "unacceptable", his spokesman said.
Reuters correspondents saw two tanks in the border town of Snizhnye in east Ukraine but said it was not clear where they had come from or whether they had previously been used by the Russian or Ukrainian army. They had no identifying markings to show whether they were Russian army tanks.
"We have observed columns passing with armoured personnel carriers, other armoured vehicles and artillery pieces, and tanks which, according to our information, came across the border and this morning were in Snizhnye," Avakov told reporters in Kiev.
He said the columns had come across the border at a checkpoint or checkpoints seized by rebels "despite the Russian Federation's statements that it welcomes the peace process and that the order has been given to strengthen border controls".
One column, Avakov said, had entered Ukraine in the Dyakove area of the Luhansk region before moving into the neighbouring Donetsk region. Ukrainian forces had confronted the column.
"There is fighting going on," he said. "Part of the column has been destroyed."
Russia did not immediately respond to the accusations and it was not clear how Putin reacted to Poroshenko by phone. His country has already been hit by U.S. and European Union sanctions over events in Ukraine and could face more.
Confirmation of direct Russian involvement in the rebels' uprising would raise the stakes in Moscow's worst standoff with the West since the Cold war ended more than two decades ago.
The separatists, who rose up after Poroshenko's predecessor was toppled and fled to Russia in February, deny receiving anything but medical supplies, food and clothing from Russia.
"Russia is helping, of course, with humanitarian aid, food, things, medicine, gear. We won't refuse that," a rebel said.
Russia has repeatedly denied providing military support to the rebels who have taken control of several towns and cities in east Ukraine and hope that Russia will annexe the region, as it did the Black Sea peninsula of Crimea in March.
Foreign Minister Sergei Lavrov had earlier on Thursday repeated Moscow's view that the onus for ending violence lay with Ukraine because it has launched a military operation against the rebels.
But he backed Poroshenko's efforts to push through a peace plan the president has drawn up and discussed with Putin.
"So far, hope remains that President Poroshenko's statements about the end of violence will be implemented and the talks start," Russia's Interfax news agency quoted Lavrov as saying.
Few details of the phone call between Putin and Poroshenko were available but the latter's spokesman wrote on Facebook that the Ukrainian leader put a heavy emphasis on the tank movements.
The presidents met for 15 minutes during World War Two anniversary events in France last week, but it was their first known conversation since Poroshenko was sworn in on Saturday.
Poroshenko has also been having meetings with a Russian envoy in Kiev and his aides say progress has been made, but talks on a long-running gas-pricing dispute have stalled.
Alexei Miller, the chief executive of Gazprom, made clear the state-run natural gas exporter would not extend a deadline for Kiev to pay its huge has debts for a third time to allow more time to reach a deal at talks.
He said a Monday deadline would stand, and Gazprom would cut supplies to Ukraine if it did not to pay off $1.95 billion of its gas debts by then. Cutting supplies to Kiev could disrupt deliveries to the European Union, which gets about a third of its gas imports from Russia, half of them via Ukraine.