By Lefteris Papadimas and Alkis Konstantinidis

KASTANIES/LESBOS, Greece (Reuters) - A child died after being pulled from the seat when a boat capsized off the Greek island of Lesbos, officials said on Monday, the first reported fatality after the Turkish government opened its border last week to let migrants reach Europe.

At least 1,000 migrants have reached Greece's Eastern Aegean islands since Sunday morning, Greek police say. More than 10,000 migrants have attempted to cross by land at the border, where guards from both sides have fired tear gas into crowds caught between the fences in no-man's land.

Turkey, which is home to 3.7 million Syrian refugees and has another million on its doorstep from a new surge of fighting, said last week it would stop enforcing a 2016 agreement that had prevented migrants from reaching the EU.

Greek officials accused Turkey of orchestrating a coordinated effort to drive migrants across the frontier.

"This movement is guided and encouraged by Turkey," government spokesman Stelios Petsas told reporters after a national security meeting in Athens. He called the surge of migrants at the border "an active, serious, severe and asymmetrical threat to the national security of the country".

Turkey's announcement last week threatens to reverse an agreement that halted Western Europe's biggest wave of migration since World War Two, the 2015-2016 crisis when 4,000 people drowned in Aegean and more than a million reached Greece.

The Greek coast guard said the boat which capsized off Lesbos on Monday morning had been escorted there by a Turkish vessel. Forty-six people were rescued and two children taken to hospital, one of whom could not be revived.

Another dinghy with about 30 Afghans arrived on Lesbos early in the morning, a Reuters journalist reported from the island. Thirty-two others were rescued in the seas off Farmakonissi, a small island close to Turkey, the coast guard said.

"This is an invasion," Development Minister Adonis Georgiadis told Skai TV on Monday.

Late on Sunday, Greek Prime Minister Kyriakos Mitsotakis tweeted that Greece was determined to protect its borders and warned migrants not to attempt to cross as security was increased to the maximum. He is expected to visit the border on Tuesday with Charles Michel, chairman of EU leadership summits.

Clashes between police and migrants broke out on Saturday and Sunday at the land border, and riot police used teargas to repel hundreds of migrants on the Turkish side.

Under a 2016 EU agreement with Turkey, Ankara agreed to stop migrants from crossing into the EU and accept most of them back if they did cross, effectively ending a crisis which toppled several EU governments and fueled the rise of the far right.

In return, the EU offered funds. But Turkey says the arrangement is in jeopardy with a new wave of Syrian refugees on its southern border, driven there by an escalation of fighting since December. Last week, at least 33 Turkish troops sent to Syria to monitor a crumbling ceasefire were killed in the Turkish army's worst attack in nearly 30 years.

The 2016 agreement halted most crossings between Greece and Turkey, although there are more than 40,000 migrants on the Aegean islands in severely overcrowded camps.

(Reporting by Lefteris Papadimas in Kastanies and by Alkis Konstantinidis on Lesbos; Editing by Peter Graff)