By Stephanie Nebehay

GENEVA (Reuters) - Russia called on Tuesday for a swift resumption of stalled Syrian peace talks, saying it was the only way to halt "massive violations" of human rights perpetrated in the five-year-old conflict.

Russia, a strong ally of Syrian President Bashar al-Assad, launched air strikes in September to support the Syrian army and its militia allies battling rebels and Islamic State fighters, and is backing an offensive on rebel-held areas of the northern city of Aleppo.

It supports proposals for a political settlement under which some Syrian opposition figures would be brought into a Syrian unity government - steps which rebels and their foreign backers say do not go far enough.

"The only way to find a solution to the Syria crisis and stop the massive violations is to promptly convene talks with a broad spectrum of Syrian opposition which includes Syria Kurds," Aleksei Goltiaev, senior counselor at Russia's mission to UN in Geneva, told the U.N. Human Rights Council.

"Only Syrians, without diktat, have the right to decide (their future)," Goltiaev said.

The main Syrian Kurdish political group, the PYD, was left out of Geneva peace talks which ground to a halt in late April without results.

Goltiaev's comments followed an appeal by United Nations war crimes investigators for world powers to pressure the warring sides to return to the negotiating table.

Paulo Pinheiro, chair of the U.N. independent commission of inquiry on Syria, said that the Syrian government was conducting daily air strikes, while militant groups including Islamic State and the Nusra Front also carried out indiscriminate attacks.

"We need all states to insist time and time again that influential states and the (U.N.) Security Council unconditionally support the political process," Pinheiro said.

U.S. ambassador Keith Harper did not refer to resumption of talks, but called for Damascus to release some of the "tens of thousands" of imprisoned Syrians. Many are subjected to "torture, sexual violence and denial of fair trials", he said.

Pinheiro said schools, hospitals, mosques and water stations "are all being turned into rubble" and tens of thousands of people were trapped between frontlines and international borders.

Syria's ambassador Hussam Aala accused regional powers of "supporting terrorism" and "causing the failure of intra-Syrian talks in Geneva".

He said schools and hospitals in Aleppo were being destroyed and civilians killed by missiles provided by Turkey and Qatar to the Nusra Front, al Qaeda's Syrian branch.

In a report last week, the U.N. investigators said that Islamic State is committing genocide against the Yazidis in Syria and Iraq to destroy the religious community of 400,000 people through killings, sexual slavery and other crimes.

"As we speak, Yazidi women and girls are still sexually enslaved in Syria, subjected to brutal rapes and beatings," Pinheiro said on Tuesday.

Vian Dakhil, the only female Yazidi member of the Iraqi parliament, told a news briefing in Geneva: "We need the Security Council to bring this report to the Criminal Court."

(Reporting by Stephanie Nebehay; Editing by Dominic Evans)