LONDON (Reuters) - British Prime Minister Keir Starmer travels to Brussels on Monday to call on Europe to shoulder more of the burden to keep the region safe from President Vladimir Putin's Russia and redouble efforts to crush his "war machine".

Starmer, in Brussels to further his post-Brexit reset with the European Union, will meet NATO Secretary General Mark Rutte and then dine with leaders from the 27 member states, the first time a British leader has done so since Britain quit the bloc.

He will urge leaders to up the pressure on Putin, saying U.S. President Donald Trump's suggestion he would add new tariffs to his sanctions threat against Moscow if there was no deal to end its war in Ukraine had rattled the Russian leader.

"We need to see all allies stepping up - particularly in Europe," Starmer will say, according to remarks provided by his Downing Street office.

"I'm here to work with our European partners on keeping up the pressure, targeting the energy revenues and the companies supplying his missile factories to crush Putin's war machine."

Since winning a landslide election in July, Starmer has worked to improve ties with the EU after years of rancorous Brexit talks, with his government hoping to agree to scrap some of red tape hampering trade to try to boost economic growth.

But on Sunday, interior minister Yvette Cooper cast doubt over one particular lever the British government could have by saying a deal for an EU-UK youth mobility scheme was "not the right starting point for us".

"We've been clear that we need net migration to come down," she told Sky News. "So that's why this is not an approach that we are looking for."

(Reporting by Elizabeth Piper; Editing by Ros Russell)