She expected Turkey in return to agree to take back migrants rejected by the EU, which Davutoglu has said he will agree to only if there is progress on the issue of visas.
"Germany is ready to offer support. If we take the question of visa liberalisation, we can talk in the German-Turkish working group about specific possibilities to push through visa facilitation," Merkel said.
The leaders agreed there could be no lasting solution to the migration crisis without resolving the conflict in Syria. More than two million refugees have now fled to Turkey.
Thousands of migrants entered Slovenia from Croatia after Hungary forged ahead with a unilateral crackdown in the absence of EU unity.
Croatia ran trains to take 4000 migrants from the town of Tovarnik on its eastern Serbian border, according to the UN's refugee agency.
Until Hungary closed its border with Croatia on Saturday, Slovenia had only received a few hundred refugees this year, said the UNHCR. More than 3000 people surged into the tiny country on Sunday alone, most intending to travel on to Austria and Germany.
The UNHCR has estimated that Slovenia has the capacity to accept around 7000 migrants a day, although Slovenian officials say they can take only 2500 a day, and that new groups will be allowed in only after previous groups leave the country.
At a station near the Slovenian border, the migrants from Tovarnik were split into groups and driven to various border crossings, before being dropped off at registration centres.
Tensions rose over the slow registration process, with 400 migrants waiting upwards of six hours at the centre yesterday and many having to queue outside.
Khalil, a 40-year-old courier, who had travelled from Homs in Syria, said: "We left Syria because of the war and genocide and massacres.
"This journey has been a bit strenuous; it's been an inconvenience; there's been much waiting ... for food, for sleeping, for clothes. It's a real misery, but what can one say."
Germany's police union chief Rainer Wendt called for a fence to be built along the country's border.
"If we want to carry out serious border controls, we must build a fence along the German border," he told German newspaper Welt am Sonntag, adding that the move would prompt other European countries which have seen hundreds of thousands of refugees cross their borders to follow suit.
Laws take aim at extremists
Extremist Islamists and hate preachers will be treated like paedophiles and banned from all contact with children in Britain, Prime Minister David Cameron was to announce overnight.
He said that defeating Islamist extremism "will be the struggle of our generation" as he reveals new laws to "disrupt" radicals operating in Britain.
He will announce sweeping new powers for the Disclosure and Barring Service to ensure that anyone with a conviction for terrorist or extremist activity is automatically banned from working with children and vulnerable people - in the same way as those convicted of sexual offences against children.
He will also announce Asbo-style restriction orders, named "extremist disruption orders", designed to restrict Islamist preachers from broadcasting, using social media or speaking at public events.
The Government will also extend powers allowing parents to apply for their children's passports to be removed if they fear they are at risk of travelling abroad to fight alongside militants such as Isis.
Under the current rules, parents can apply to have the passports of under-16s removed by the authorities. This will be extended to under-18s.
