Russian president Vladimir Putin would see Britain's exit from the EU as a sign of "weakness", shadow foreign secretary Hilary Benn has warned.
Mr Benn highlighted global political dangers as he insisted the case for staying in is "stronger than ever".
But Vote Leave, one of the groups campaigning for an exit, accused him of resorting to scare tactics.
It comes as Foreign Secretary Philip Hammond said the UK still has "issues" with a proposed EU reform package.
"There is no deal at present; there is a working draft," he said.
"We have issues, some of which have been addressed - language issues - in the latest iteration of the draft, some of which have not been addressed," Mr Hammond told reporters in Brussels.
"So the discussions continue and I do not think it is sensible to draw any conclusions about the shape of the deal until we see the final text that emerges from the European Council meeting," he added.
David Cameron is hoping to secure a deal on the proposed reforms at the EC meeting in Brussels next week, paving the way for a referendum on the UK's membership of the EU in June.
Delivering a speech at the Chatham House think-tank in London, Hilary Benn said leaving the European Union would mean the UK was less able to deal with international challenges such as the migrant crisis and climate change.
Referring to Russian action in the Crimea and Ukraine, Mr Benn said it was down to "Europe's collective response that we have been able to exert real pressure and have an impact".
"Efforts towards the creation of an EU-wide energy union will, over time, weaken Russia's dominance as an energy supplier in Europe," he added.
"Let's be clear. President Putin would shed no tears if Britain left the European Union. He would see Brexit as a sign of our weakness and of the weakness of European solidarity at the very moment when we need to maintain our collective strength."
Matthew Elliott, chief executive of the Vote Leave campaign, hit back at Mr Benn's claims.
"Pro-EU campaigners cannot make a positive case for remaining in a political project that is incapable of dealing with the challenges of the 21st century," he said.
"Instead of accepting that we need a new relationship with the EU, they are whipping up fear about dictators and economic doom despite the fact that neither are remotely credible.
"Voting Leave is the safe option as it will allow us to make our own trade deals, end the supremacy of EU law and invest in our priorities."
Mr Benn also used his speech to restate his position on the replacement of Britain's Trident nuclear weapons, which are at odds with those of his party's leader Jeremy Corbyn.
He said other nuclear powers would not throw their missiles "in the dustbin" if the UK unilaterally disarmed.
"I think you get there by multilateral negotiation and not by unilateral action," he said.
"If we gave ours up I don't believe for a second that any one of the other nuclear powers in the world would say 'well if you're not going to keep yours any more we'll throw ours in the dustbin'."
Labour is carrying out a review of its defence policy, including whether Trident should be renewed.