The European Commission has accused Belarus's authoritarian leader of luring migrants with the false promise of easy entry to the EU as part of an "inhuman, gangster-style approach". At least 2,000 migrants are now at the Belarus border with Poland. "Upon arrival they are being pushed to the border and forced to make an illegal entry into the European Union," said Commission spokesman Peter Stano. Belarus's leader Alexander Lukashenko denies orchestrating the problem. EU and Nato members Poland, Lithuania and Latvia have all seen a surge in the number of people trying to enter their countries illegally from Belarus in recent months. Many are young men but they include women and children, largely from the Middle East and Asia. Poland has seen the most arrivals, especially around its major border crossing at Kuznica. Migrants have described how Belarusian authorities seized their phones and pushed them towards the border fence. Overnight temperatures at the border have slumped below zero and several people have already died in recent weeks. "Nobody is letting us get in anywhere, Belarus or Poland," 33-year-old Shwan Kurd from Iraq told the BBC by video-call. He described how he had arrived in Minsk from Baghdad at the start of November, and was now in a make-shift camp metres from Poland's barbed-wire fence. "There's no way to escape," he said. "Poland won't let us in. Every night they fly helicopters. They don't let us sleep. We are so hungry. There's no water or food here. There are little children, old men and women, and families." Poland has deployed extra troops after desperate crowds tried to cut the border fence on Monday. The border guard said more than 300 attempts had been made to cross illegally. The government warned of a possible "armed" escalation on its border with Belarus, fearing its neighbour might try to provoke an incident. The head of Poland's national security department, Stanislaw Zaryn, said the migrants were under the control of Belarusian armed units. "Belarus wants to cause a major incident, preferably with shots fired and casualties," deputy foreign minister Piotr Wawrzyk said on Monday. The EU, Nato and the US all say Belarus is orchestrating the problem. Brussels accuses Belarus's disputed leader, Mr Lukashenko, of provoking the influx in retaliation against EU sanctions. Those sanctions were imposed after Mr Lukashenko's widely discredited re-election in August last year and subsequent crackdown on mass protests. Addressing parliament on Tuesday, Polish Prime Minister Mateusz Morawiecki suggested Russian leader Vladimir Putin - a close ally of Mr Lukashenko - had had a hand in orchestrating the wave of migrants. In an interview with the Belarusian state news agency, Mr Lukashenko said he wanted to avoid any military escalation on the border which could draw Russia into a conflict.He said he was "not a madman" but he remained defiant, saying "we will not kneel down". The Belarus defence ministry rejected the Polish statements as unfounded and unsubstantiated, and accused Warsaw of violating agreements by moving thousands of troops to the border. Belarus insists the migrants are arriving legally there and that it is merely acting "as a hospitable country". Russia has praised its ally's "responsible" handling of the border row and said it is watching the situation closely. Later on Tuesday, Lithuania declared a state of emergency in its border region with Belarus, the first time the Baltic nation has done so. Lithuania's interior minister Agne Bilotaite said this was a precautionary measure taken in response to events on the Belarusian-Polish border. The measure was backed by MPs and will come into force at midnight, imposing restrictions on movement in the border region. Activists say the migrants are being used as pawns in a political game between non-EU Belarus and its neighbours. Poland has also been accused of pushing migrants back across the border, contrary to international rules of asylum. The UN refugee agency's spokesperson Shabia Mantoo said it was very worried by the latest scenes: "Using refugees, asylum seekers and migrants to achieve political ends is unacceptable and must stop." BBC correspondent Nick Beake who is near the border says Polish authorities are strictly enforcing a state of emergency in the area. It means independently verifying what's happening in this escalating migrant crisis is difficult, he says. The European Commission is now looking to extend sanctions to include "third-country airlines" involved in flying migrants to Belarus. It said it was looking at flights to Minsk from a number of countries, including Syria, Iran and Qatar as well as Russia and several North African states. Germany on Tuesday urged the EU to "take action" to help Poland secure its borders. Lithuania has also moved troops to its border with Belarus to prepare for a possible influx of migrants.