Thousands of migrants remain stranded at Budapest's main international railway station as authorities stick to EU rules and prevent them from leaving for Germany and other countries west of Hungary.

Around 3,000 migrants are at Keleti station in the Hungarian capital, many camping outside the main entrance guarded by police, who said citizen patrols were assisting them in keeping order.

Volunteer groups accustomed to providing food, clothing and medical assistance to a few hundred migrants at a time struggled with the large number of people staying in every corner of the station's sunken plaza.

More than 150,000 migrants have reached Hungary this year, most coming through the southern border with Serbia. Many apply for asylum but quickly try to leave for richer EU countries.

Hungary's police said they intend to reinforce their positions outside the terminal as the volume of migrants arriving from Serbia continues to grow by the hour.

They said officers working jointly with colleagues from Austria, Germany and Slovakia also were searching for migrants travelling illegally on other Hungarian trains and described the security push as compatible with the EU's policy of passport-free travel.

Meanwhile, at least 11 migrants have died and five others are missing after boats carrying them to the Greek island of Kos capsized.

A boat carrying 16 people sank in international waters after leaving from the Turkish resort of Bodrum. Seven of them drowned while four were rescued.

Hours later, a second boat carrying six migrants sank off the coast of Bodrum. A woman and three children drowned while two migrants in life jackets made it to shore half-unconscious, the report said.

The route between Bodrum and Kos is one of the shortest from Turkey to the Greek islands. Thousands of migrants are attempting the perilous sea crossing despite the risks.