About 2,000 migrants, mainly Kurds from the Middle East, have been stuck for days on the border in near-freezing temperatures, with the WHO saying on Friday it was "very concerned" about their plight.
US vice president Kamala Harris said Lukashenko was "engaged in very troubling activity" and warned that "the eyes of the world and its leaders are watching."
Steps were being taken to stem the flow of migrants, with Ankara saying that Iraqis, Syrians and Yemenis would no longer be allowed on flights from Turkey to Belarus.
Iraq said it was drawing up lists of its citizens blocked on the border who wanted to go home and was ready to organise repatriation trips. It had also closed Belarusian diplomatic missions that had been providing Iraqis with tourist visas.
"We are seeing progress on all fronts," European Commission vice president Margaritis Schinas told a press conference in Lebanon, adding that he would soon be travelling to Iraq and Turkey.
Warning to 'hotheads'
A German foreign ministry spokeswoman said talks were continuing with airlines and countries along possible migrant routes, and that the Turkish ban showed "we already have some success".
Amid reports this week of more flights from Turkey and the Middle East carrying migrants to Minsk, Western countries are demanding Lukashenko and his main ally Russia take steps to end the crisis.
The US and European delegations at a UN Security Council meeting on Thursday accused Minsk of endangering lives for political purposes and trying to divert attention "from its own increasing human rights violations".
Minsk and Moscow have accused EU countries of failing to live up to international standards by blocking the migrants, who they say are seeking shelter after Western military "adventures" in the Middle East.
In a show of support for Minsk, Russia has sent strategic bombers to patrol over Belarus this week and on Friday the two countries said a joint battalion of paratroopers was holding snap drills near the Polish border.
"The Belarusian armed forces are ready to respond harshly to any attacks," Belarusian Defence Minister Viktor Khrenin said.
"We'd like to warn hotheads against overestimating their capabilities," he said, stressing Russia was ready to help ensure Belarus's security.
Tensions are already high between Moscow and the West over Ukraine, with US and EU leaders in recent days raising concerns over reported Russian troops movements near the Ukrainian border.
Moscow has rejected any claims it is involved in the Belarus migrant crisis, with president Vladimir Putin telling Europe it should "restore contacts" with Minsk if it wants a resolution.
The EU is instead considering new measures against Lukashenko, who is already under sanctions for a severe crackdown on opponents after a disputed presidential election last year.
Kremlin vows no gas cut
The Belarusian leader, who has ruled the ex-Soviet country for nearly 30 years, suggested Belarus could cut off a gas pipeline to Europe in response.
The Kremlin dismissed the threat on Friday, saying Russia's reliability as a gas supplier "is beyond question".
Poland has moved 15,000 troops to the Belarus border, put up a fence topped with barbed wire and approved the construction of a wall.
Migrants have been trying to cross the border for months but the crisis came to a head when hundreds made a concerted effort on Monday and were pushed back by Polish border guards.
They set up a camp on the border where hundreds are sheltering in tents and burning wood from local forests to keep warm.
At least 10 migrants have died on the border in recent months, seven of them on the Polish side, according to Polish newspaper Gazeta Wyborcza.
It is unclear how many migrants are now in Belarus but thousands have crossed or attempted to cross from the country into the eastern EU states of Latvia, Lithuania and Poland since the summer.
WHO Europe director Hans Klug said he was "very concerned about the thousands of vulnerable people who are stranded in no-man's land.... at the mercy of the weather as winter fast approaches."