Hungary took out a full-page advert in a Lebanese newspaper to deter refugees from setting off for Europe, as hundreds more reached the continent's shores while several died on the way.

The ad placed by the right-wing government or prime minister Viktor Orban in Lebanon's leading daily An-Nahar warned asylum seekers that illegal crossing into Hungary is now a crime punishable with jail.

"Hungarians are hospitable but the strongest possible action is taken against those who attempt to enter Hungary illegally," the message read. "Do not listen to the people smugglers. Hungary will not allow illegal immigrants to cross its territory."

Under new regulations entered into force last week, migrants and refugees entering the country illegally or damaging its hastily erected border fences – which are four metres high and 110 miles long – carries a possible three-year jail term. Such sentences also carry a further burden for refugees, providing them with a criminal record that might hamper their chances to secure asylum in another EU country.

Earlier in September, Denmark also placed advertisements in four Lebanese newspapers warning that it had introduced tighter regulations and cuts in provisions for asylum seekers in a bid to stem the inflow. Meanwhile thousands more fleeing war and poverty in the Middle East and Africa arrived in Europe.

The Italian coastguard said it rescued 4,343 migrants on 20 different vessels off the Libyan coast on 19 September and found the dead body of a woman aboard a rubber dingy. Another three boats carrying 610 people were intercepted the next day.The high influx came after a few days of rough seas that saw no arrivals in the Mediterranean country.

Greek authorities said they have rescued 994 people at 42 different locations over weekend and pulled from the waters the lifeless bodies of two girls and a woman. Coastguard vessels were still searching for up to 36 people that are missing after two vessels separately sank off the island of Lesbos.

Meanwhile, a series of high-profile meetings to discuss the crisis at EU level are due to take place this week. EU interior ministers are planned to hold talks on 23 September while an extraordinary summit of EU leaders is planned for the next day.

More than 430,000 migrants have arrived in Europe since January, according to the International Organisation for Migration (IOM). Most have crossed from Turkey to Greece and then proceeded north through the Balkans.

Austrian police said almost 24,000 have crossed into the country from Hungary at the weekend , while the situation remains problematic across Serbia, Hungary, Croatia and Slovenia as thousands try to find a point of entry to the EU.