A Syrian rebel forces spokesman said the towns were surrounded after fighters seized the villages around them.
A Kurdish-led group and Syrian activists claimed Thursday that despite the bombardment, Turkish troops had not made much progress on several fronts they had opened over the past hours.
European diplomats in Brussels have responded cautiously to the idea of sanctions on Ankara though the invasion - which began Wednesday and was dubbed by Turkey "Operation Peace Spring" - has met with unanimous criticism.
Muhammad Yusuf Hussein and his seven-year-old sister Sarah were hit in a strike on Qamishli, the de facto capital of the unrecognised Kurdish statelet of Rojava.
In Syria, residents fled with their belongings loaded into cars, pickup trucks and motorcycle rickshaws, while others escaped on foot.
A statement co-signed by the organisations - including Doctors Without Borders, Oxfam and the Norwegian Refugee Council - said an estimated 450,000 people live within three miles of the Syria-Turkey border and "are at risk if all sides do not exercise maximum restraint and prioritise the protection of civilians".
Turkish President Recep Tayyip Erdogan announced the beginning of the so-called Operation Peace Spring Wednesday with an eye to creating a safe zone near the Syrian-Turkish border, clearing up "terrorists" and ensuring a safe return for the Syrian refugees now hosted in Turkey.
The Turkish Government considers members of the Kurdish militia to be "terrorists" due to their links to the outlawed Kurdistan Workers' Party (PKK), which has led an insurgency against Turkey for 35 years.
He also reiterated a plan to settle millions of Syrian refugees in the "safe zone" in northeastern Syria, saying Turkey aimed to realise this with worldwide funding. It says it has killed 277 militants in total.
The International Rescue Committee aid group says 64,000 people in Syria have fled in the first days of the campaign.
The YPG have been allies of the USA so far in the fight against the jihadist group Islamic State, but Ankara considers it a terrorist organization for its links with the banned Kurdistan Workers Party, the active Kurdish guerrilla in Turkey. The US and Russian Federation were notably absent from the list.
Officials claim that since the phone call, various diplomatic exchanges between the U.S. and Turkey, involving President Erdogan have taken place.
Following the news of the offensive and the threat towards Kurds in northern Syria, Trump warned the Turkish President, that he "will wipe out his economy if that happens".
The Syrian Kurdish militia was a USA ally in the campaign that brought down the Islamic State group in Syria.
The U.N. Security Council is discussing a US -drafted statement, but it appeared unlikely they could reach an agreement.
Sen. Lindsey Graham (R-SC) - a typically steadfast Trump backer but one of the most outspoken opponents of the American withdrawal - on Thursday unveiled the framework for a potential package of sanctions with Maryland Democratic Sen.
The ministry's communique called on the worldwide community, as well, to live up with what the statement termed "responsibility towards regional and global peace and security".
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As he spoke, 29 members of Trump's Republican party in the House of Representatives announced that they would introduce legislation to impose sanctions on Ankara for its actions in northern Syria.