EU chief diplomat Josep Borrell said the compromise between bickering member states would "significantly reduce" the number of Russians being granted access to the passport-free Schengen zone.
Diplomats from northern and eastern Europe had lobbied for stricter rules to deal with the galling sight of Russian shoppers and luxury cars crossing their borders while missiles fall on Ukraine.
But many EU members objected to a ban on the grounds that it would close the door to Russian dissidents or play into the hands of Kremlin propaganda.
After hours of talks at a meeting of EU foreign ministers in Prague, Mr Borrell said the bloc's 27 members had agreed that "something has to be done" to address the swelling number of visitors.
"We have seen many Russians travelling for leisure and shopping as if no war was raging in Ukraine," he said. "It cannot be business as usual."
Although some border states such as Finland and Estonia have brought in curbs on tourism, they cannot close the door unilaterally because Russians can use a Schengen visa issued by any member of the passport-free zone.
As a first step, the suspension of the so-called visa facilitation agreement will put extra bureaucratic hurdles in the way of Russian tourists who apply for tourist visas in Europe.
"It’s going to be more difficult, it’s going to be longer, the process, and consequently the number of new visas will be substantially reduced," said Mr Borrell, after agreement was reached in principle to suspend the deal.
However, EU members also agreed that visas should continue to be granted in individual cases to Russians who represent civil society or oppose the war in Ukraine, he said.
The European Commission was told to draw up proposals for how to address the number of Russians, thought to be in the millions, who already have visas for the Schengen zone.
A rush of summer visitors has seen Helsinki Airport fill up with Russian-registered luxury vehicles, exploiting the open land border to work around a flight ban imposed in March.
“At the same time when Ukrainians are suffering, normal tourism shouldn't continue,” said Finnish Foreign Minister Pekka Haavisto, who was among those lobbying for stricter rules.
“Now that the air connections have been cut, there is more and more of this tourist route through Helsinki Airport … we are not looking at that very favourably.”
Latvian minister Edgars Rinkevics said Russian visitors were potential security risks, citing the examples of Russian operatives who carried out attacks in Britain, the Czech Republic and elsewhere in recent years.
Denmark took the position that it was unreasonable to let Russian men have a good time in Europe when their Ukrainian counterparts are required to stay in the country to fight.
However, some countries rejected the arguments made by Baltic states and said it would be unfair to potential allies in Russia to stop them from coming to Europe.
“We have always said that it is Putin's war, not the Russian people's war,” said Luxembourg's Foreign Minister Jean Asselborn.
Foreign Minister Annalena Baerbock, representing Germany, said applications from Russia had fallen of their own accord but that Schengen visas had sometimes been useful in spiriting dissidents out of the country.
Ukraine conflict — in pictures
France said a ban would miss its desired target since wealthy oligarchs closely tied to the war effort had already been banned from entering the EU in seven existing rounds of sanctions.
Diplomats also heard the argument, advanced by France, Germany and Romania among others, that letting Russians into Europe would give them a valuable taste of freedom.
The talks came hours after news broke of the death of former Soviet leader Mikhail Gorbachev, and many politicians remarked on the poignant timing as Russia becomes increasingly isolated.
“We have to be very careful in order not to block the possibility for exposing the young generation in Russia to European values,” said Romanian minister Bogdan Aurescu.
Mr Rinkevics, for Latvia's part, dismissed that argument.
“I do not take seriously the argument that by visiting Europe, Russians will learn a lot how to change their country,” he said. “They have had 30 years of visits.”