NATO head Jens Stoltenberg and European Commission chief Ursula von der Leyen made the pledges during a visit to Latvia and Lithuania ahead of a meeting of NATO foreign ministers in Latvia this week.
EU and NATO leaders have vowed to counter "hybrid threats" on visits to Lithuania and Latvia dominated by the Belarus migrant crisis and Russia's military build-up near Ukraine.
"To respond to such events, it is important that the European Union and NATO work hand in hand," European Commission chief Ursula von der Leyen said at a joint news conference with NATO chief Jens Stoltenberg and Lithuanian leaders on Sunday in Vilnius.
"We discussed how we could step up our joint work between NATO and the EU," said Stoltenberg.
Stoltenberg also repeated his call on Russia to "de-escalate" its military build-up on the border with Ukraine and warned of "consequences" if it used force.
He said the "unusual" build-up of tanks, artillery, drones and thousands of combat-ready troops was "very concerning for many reasons", also "because it is unprovoked and unexplained".
Stoltenberg and von der Leyen both accused Belarus of orchestrating the migrant crisis on its border as a "hybrid" threat against the European Union - a charge that the regime has denied.
A hybrid threat is a security challenge combining traditional military means and non-military tactics such as disinformation.
READ MORE: EU to widen sanctions against Belarus
EU to triple funding
Von der Leyen also said the EU had decided to triple to $226 million its funding for border management in Latvia, Lithuania and Poland for 2021 and 2022.
She said the money would go on patrol vehicles and electronic surveillance, including drones.
Thousands of migrants, mostly from the Middle East, have crossed or tried to cross the Belarus border in recent months into the eastern members of the EU and NATO: Latvia, Lithuania and Poland.
Referring to the situation on the Belarus border, Lithuanian President Gitanas Nauseda said that "if the security situation gets even worse, we do not rule out consultations under NATO's Article 4".
Under the article in NATO's founding treaty, any member can convene a meeting of the alliance to consult when it feels its security threatened.
Poland has also said it may invoke this article.