Fighting between Islamic State (IS) militants and Syrian Kurds is reported to have spread to a southern district of the town of Kobane on the Turkish border, as US-led air strikes continue.But fighting in the town was less intense than on Monday, when IS took control of three districts in the east.
Witnesses report several loud explosions and plumes of smoke from coalition air strikes.
More than 160,000 Syrians, mainly Kurds, have fled Kobane recently.
Turkish Prime Minister Recep Tayyip Erdogan said the town was on the verge of falling and "co-operation" on a ground offensive was necessary.
If IS captures Kobane, its jihadists will control a long stretch of the Syrian-Turkish border.
In the latest clashes, the Syrian Observatory for Human Rights (SOHR) activist group said IS had crossed into a southern district of Kobane, taking over many buildings.
However, the group said heavy fighting had forced IS to pull back in eastern districts. It also suggested many IS fighters had been killed in an ambush by Syrian Kurdish fighters.
At least 400 people have been killed in three weeks of fighting for Kobane, according to the SOHR's latest estimate.
He also repeated the Syrian Kurds' appeal for the West to supply weapons, and called for coalition aircraft to "strike more effectively". Mr Nassan said the Kurds had not yet received "any suitable answer".
On Monday, IS took control of Mistenur, the strategic hill above Kobane after heavy shelling.
There was constant gunfire and a steady stream of Turkish ambulances racing to and from the border, with many wounded people being treated in hospitals close to the frontier.
A humanitarian mission to evacuate the few thousand civilians left in Kobane continued on Tuesday.
Karwan Zebari, a representative of the Kurdish regional government in the US, is among those urging Turkey to take action.
"If this continues, if there's no international aid, military aid arriving for the residents of Kobane and these Kurdish fighters that are fighting in Kobane, it could fall into the hands of IS," he told the BBC.
In Turkey, Kurds angered at the government's reluctance to intervene clashed with police overnight in several cities, including Istanbul.
Turkish Kurds and refugees have been involved in confrontations with Turkish security forces on the border for the past two days.
Last week, Turkey pledged to prevent Kobane from falling to the militants and its parliament authorised military operations against militants in Iraq and Syria.
Turkey - a regional superpower with significant troops and armour in the area - seems extremely reluctant to intervene despite a government pledge to do whatever it takes to prevent the Kurdish town of Kobane from falling.
It wants the US-led coalition to agree on a number of things first, including setting up a no-fly zone and a buffer zone in northern Syria and, crucially, a renewed focus on getting rid of President Assad - which remains Turkey's principal objective.
Add to that the very bad blood that has existed for decades between Turkey and its own Kurdish population.
Turkey fought a bloody war against the Turkish guerrilla group, the PKK, that helps to explain why Ankara remains deeply reluctant to get engaged.