© Reuters / Petr JosekPeople wait at a customs post at the renovated pedestrian crossing between Slovakia and Ukraine at the east Slovakian village of Velke Slemence.
"We can speak of thousands of illegal migrants from Ukraine who are motivated to cross the Schengen borders in our or other zones," said Slovakian Prime Minister Robert Fico at the GLOBSEC annual conference in the country's capital, Bratislava, reported Itar-Tass.
Meanwhile, organized criminal groups have recently been stepping up illegal transportation of migrants across the Slovak-Ukrainian border, according to Mr Fico.
Slovakia borders Ukraine's Transcarpathia region in the West. This is Ukraine's shortest border - only 98 km long.
In February, Jozef Danko, spokeman for the Slovakian village of Vysne Nemecke on the border with Ukraine, told Voice of Russia radio that the inflow of vehicles from Ukraine has recently increased, not only from the nearest cities which border Vysne Nemecke but also from other parts of Ukraine.
"If earlier there were many cars from Uzhhorod [Ukrainian city] and Transcarpathia [region], now there are more cars from Kiev," he added.
In April, Russia's Federal Border Guard Service said it was monitoring the flow of migrants from Ukraine.
"For the last two months we have been monitoring the increase of Ukrainian citizens applying for various statuses which allow them to stay in Russia. There are refugees, and forced migrants...," said Konstantin Romodanovsky, the head of the service.
Sanctions will be a major blow to European economy
On Thursday, the Slovakian prime minster spoke against the third round of sanctions on Russia.
"I'm very skeptical about the third level (of sanctions), because if we look at the position of some other EU members, we see strong hesitation," Fico said.
Slovakia will also suffer from these sanctions as they would cut the country's growth to at least 1 percent in 2015 from an expected 3.1 percent.
"It will be a major blow, not only to the European economy, but especially to the economies of the countries neighboring Ukraine," he added.
The unwanted people in Ukraine are fleeing the Fascist Coup Government. They know what Kiev wants to do to them.