More than a thousand people have reached the former Yugoslav republic of Macedonia after leaving an overflowing refugee camp near the northern Greek border.

The group arrived in Moine, 5km inside Macedonia, on Monday, according to the Macedonian television station TV Sitel.

The refugees marched away earlier from the tent city near Idomeni, where at least 12,000 people have been stranded in filthy conditions since Macedonia and other nations blocked their route north along the so-called Western Balkan route.

Images from the border showed hundreds of refugees wading through a narrow river stream to reach Macedonia.

Later, a second group of 500 refugees set off from Idomeni to follow them.

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They were trying to find a gap in the barbed-wire fence that Macedonia has built along its border to deter the refugees, many of whom come from warzones in Syria and Iraq.

They want to head north to wealthier European Union nations such as Germany.

Late on Monday, police in Macedonia said they would take steps to return the refugees to Greece.

"Police and army have heightened security on the border at critical points," the Macedonian police spokesperson said.

She said she believed "several hundred" people had crossed the border, lower than an estimate of 2,000 made by a Reuters photographer earlier.

Long cavalcade

Heading west from the camp in a long, snaking cavalcade along muddy paths, the refugees, wearing coats and hats, carried their belongings in rucksacks and bags.

The group included many children, some walking, others on strollers.

Some of the refugees made victory signs as they walked along.

There was no sign of police following the refugees.

When they reached Crna Reka river, the refugees passed a rope across it and formed a "human chain" to cross.

Several people carried children across on their shoulders.

After crossing the Crna Reka near the village of Hamilo, the refugees reached the border fence and walked along it trying to find a way through into Macedonia.

Earlier, Macedonian police said two men and a woman drowned while trying to cross a river close to the Greek border that had been swollen by heavy rain.

Greece has stepped up efforts to move thousands of refugees near the Macedonian border to sheltered camps amid fears about the spread of infectious diseases.

EU leaders and Turkey are due to meet again on Thursday and Friday to seal a deal to try to check the refugee flow from Turkey to Europe through Greece.