Kyiv - Russian troops are being pushed away from Ukraine’s second city Kharkiv, President Volodymyr Zelensky said, but sounded a note of caution as Washington said Vladimir Putin won’t stop with the east and is ready for a long war.

Following that bleak prediction, and after President Joe Biden warned that Ukraine would likely run out of funds to keep fighting within days, the US House of Representatives voted Tuesday to send a $40 billion aid package to the country.

The US Senate is expected to rubber-stamp the decision by the end of this week or next, a show of rare bipartisan support that would bring total US help to Ukraine to around $54 billion.

“With this aid package, America sends a resounding message to the world of our unwavering determination to stand with the courageous people of Ukraine until victory is won,” House Speaker Nancy Pelosi told her Democratic colleagues ahead of the vote.

In his nightly address on Tuesday, Zelensky said he had “good news” from the northeastern Kharkiv region. “The occupiers are gradually being pushed away,” he said. “I am grateful to all our defenders who are holding the line and demonstrating truly superhuman strength to drive out the army of invaders.”

The head of the Kharkiv regional state administration Oleg Synegubov said on Telegram that “fierce battles” were ongoing in the region, and that the city itself was under heavy fire.

“Due to successful offensive operations, our defenders liberated Cherkasy Tyshky, Rusky Tyshky, Rubizhne and Bayrak from the invaders,” he said.

“Thus, the enemy was driven even further from Kharkiv, and the occupiers had even less opportunity to fire on the regional centre.”

Despite the apparent headway made, Zelensky urged Ukrainians not to “create an atmosphere of specific moral pressure, when certain victories are expected weekly and even daily”, a reflection of the intense pressure being exerted by Russia on its neighbour.

A stark example of that could be seen in the Kharkiv region itself, where Synegubov announced that 44 civilian bodies had been found under the rubble of a destroyed building in the eastern town of Izyum, now under Russian control.

Since trying and failing to capture Kyiv in the first weeks of the invasion in late February, Moscow has moved its focus to the Russian-speaking Donbas region in the east.

But on Tuesday US Director of National Intelligence Avril Haines said the decision to concentrate Russian forces there was “only a temporary shift”.

“We assess President Putin is preparing for prolonged conflict in Ukraine during which he still intends to achieve goals beyond the Donbas,” Haines said, adding US intelligence thinks he is determined to build a land bridge to Russian-controlled territory in Moldova.

A path to achieving that goal would be taking the southern city of Odessa, where missile strikes have destroyed buildings, set ablaze a shopping centre and killed one person, as well as interrupting a visit by European Council President Charles Michel on Monday.