BRUSSELS (AP) — European Union leaders on Tuesday hailed the presidential election in Ukraine and called on Vladimir Putin’s Russia to do what it can to end the fighting in the country’s east.

Leaders of the 28 EU countries, meeting in Brussels, said they expect Russia to cooperate with Ukraine’s “newly elected and legitimate president,” Petro Poroshenko, winner of Sunday’s elections.

If Moscow doesn’t cooperate or fails to help halt the fighting, it could face stiffer economic sanctions, French President Francois Hollande said.

“President Putin must now not only respect the (election) outcome but also recognize the Ukraine president and make sure there is a de-escalation, which is expected and possible today,” Hollande said.

In a statement, the EU heads of state and government said that as a priority, Russia should prevent separatists and weapons from crossing the border into Ukraine. Russian troops should also continue to withdraw from areas near Ukraine, where NATO has said they have been exerting a coercive influence, the leaders said.

“We encourage the Russian Federation to enter into a frank and open dialogue” with Ukraine’s government, the leaders said.

The EU and Russia have been at odds over Ukraine for months. The refusal of its former elected president to enter into an association agreement with the trade bloc and opt instead for closer ties with the Kremlin sparked large protests that drove him from office, and set the stage for Russia’s unilateral annexation of Crimea.

The EU has imposed limited asset freezes and visas bans on people linked to the Crimea takeover and the pro-Russian revolt in Ukraine’s east. Hollande said tougher measures could be imposed by the West based on Moscow’s future actions.

“The threats of sanctions are still there,” Hollande told a news conference. He noted he had invited Putin to visit France on June 6, the 70th anniversary of the D-Day landings, and said, “at that time we will hold talks.”

In their statement, the EU leaders pledged continued assistance to Ukraine, and said they were looking forward to “working closely” with Poroshenko. But they said Ukraine must do more to fight corruption, reform the judiciary and police and improve the business climate.

To help Ukraine, the European Union has already disbursed the first installment of macro-financial assistance totaling 1.61 billion euros ($2.2 billion). On Tuesday, the EU’s executive arm recommended a further step toward ultimately allowing visa-free travel by Ukrainian citizens.

Copyright 2014 The Associated Press.