Get breaking news alerts and special reports. The news and stories that matter, delivered weekday mornings.

An influx of Syrians flocked to the Turkish border on Saturday, but officials in Turkey say any displaced refugees would not be allowed into their country except in the case of extreme "crisis."

As many as 35,000 Syrians had massed along the closed border in the last 48 hours, a Turkish official said Saturday, according to The Associated Press.

But a source from the office of Turkey's prime minister told NBC News that the border would likely not be opened because the Turkish government worries that the mostly-Sunni refugees will settle in villages and towns with differing religious groups.

Suleyman Tapsiz, governor of the border province of Kilis, said Turkey would send aid, but would only let the Syrians cross into the country in the event of an "extraordinary crisis."

The Norwegian Refugee Council said thousands of Syrians have arrived at seven of the main informal camps close to the Turkish border. The group said the camps were already at capacity before the latest influx, and that aid groups are working around the clock to deliver tents and essential items to the displaced.

The latest movement of refugees and migrants comes as Aleppo inches closer to falling under a government siege, cutting thousands off from aid while Russia bombards the city with airstrikes.

"In many respects, a siege of Aleppo has in fact happened," U.S. State Department spokesman John Kirby said Friday.

Related: New Syria Crisis: Tens of Thousands Flee 'Siege of Aleppo'

Let our news meet your inbox. The news and stories that matters, delivered weekday mornings. This site is protected by recaptcha

Aleppo, which was Syria's commercial hub before civil war broke out in 2011, is split between government and rebel control. Russia, which joined the conflict to aid Syrian President Bashar Assad in September, has in recent days intensified aerial attacks on the city, leaving 150 civilians dead, according to Samantha Power, the U.S. ambassador to the United Nations.

The week had begun on a somewhat hopeful note, with U.N. envoy Staffan de Mistura declaring the launch of indirect talks between a Syrian government delegation and opposition representatives in Geneva.

However, he was forced to adjourn by mid-week, after the opposition said there was no point negotiating while pro-government troops were backed by the Russian airstrikes.

The breakdown of the talks was followed by a warning from opposition backer Saudi Arabia that it is ready, in principle, to send ground troops to Syria, albeit in the context of the U.S.-led military campaign against ISIS extremists who control large areas of Syria and Iraq.

Russia's Defense Ministry meanwhile said it had "reasonable grounds" to suspect that Turkey, another opposition ally, is making intensive preparations for a military invasion of Syria.

Syrians gather at the Bab al-Salam border gate with Turkey, in Syria, Saturday, Feb. 6, 2016. Bunyamin Aygun / AP

Syria's Foreign Minister Walid al-Moallem warned Saturday that Saudi or other foreign troops entering his country would "return home in wooden coffins" and asserted that recent military advances put his government "on track" to end the five-year-old civil war.

"I can say, from the achievements for our armed forces ... that we are now on track to end the conflict," he said. "Like it or not, our battlefield achievements indicate that we are headed toward the end of the crisis."

Walid al-Moallem called on rebel fighters to "come to their senses" and lay down their weapons.

Asked about the possibility of Saudi ground troops entering Syria, he said logic would suggest this is unlikely, but that "with the crazy Saudi leadership nothing is far-fetched."

The U.N. envoy, de Mistura, has said the Geneva talks should resume by Feb. 25, though it's unclear if the delegations will return.

The opposition has accused the government of acting in bad faith by launching the Aleppo offensive in parallel to the start of the talks.