German Chancellor Angela Merkel on Sunday held talks with Turkish leaders in Istanbul to promote a European Union plan that would offer aid and concessions to Turkey in exchange for measures to stem the mass movement of migrants across Europe's borders.

Her discussions with Prime Minister Ahmet Davutoglu and President Recep Tayyip Erdogan come at a time when thousands of new arrivals a day are stretching Germany's capacity to house refugees and other migrants.

Officials said the EU incentives offered to Turkey would involve an aid package of at least 3 billion euros ($3.4 billion) to help Turkey host the more than 2 million refugees who are currently in the country, as well as easier access to EU visas for Turkish citizens and re-energized EU membership talks.

The EU plan would see Turkey improve its asylum and documentation procedures and beef up border and coast guard numbers. The idea is to help stop people entering Turkey in search of work there or in the EU, and then prevent both them and refugees already in the country from moving on to Europe.

Turkish officials said this week that the plan was still a "draft" and nothing had been agreed yet.

Erdogan vented his grievances with Europe this week, pointedly taking swipe at talk of awarding Merkel the Nobel Peace Prize for welcoming hundreds of thousands of migrants.

"We have 2.5 million refugees. No one cares," Erdogan said.

Amnesty International voiced concerns over the plan and has called on Merkel and EU leaders to put the rights of refugees above concerns to protect their borders. It said the plan ignores the "challenges" the refugees face in Turkey and the "need for the EU to offer protection to a greater share of the world's burgeoning refugee population."

In a statement released Saturday, the human rights advocacy group said the EU should look for ways to provide safe routes for the refugees trying to reach Europe.

Apart from the migrant crisis, the Turkish and German leaders will also be discussing the fight against terrorism and the situation in Syria.

Last week, two suicide bombings targeting a peace rally in the Turkish capital Ankara killed 102 people. Unconfirmed reports say the attacks were carried out by a Turkish cell of the Islamic State group.