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WRAPUP 9-Ukraine says all women, children now evacuated from Mariupol steel mill

(Adds Zelenskiy comments in Saturday night address)

* Women, children and elderly evacuated, deputy PM says

* Not clear if other civilians remain

* Russian forces try to storm Azovstal, Ukraine military says

* CIA director says Putin 'doubling down' on conflict

* WHO documents 200 attacks on healthcare facilities in Ukraine

By Pavel Polityuk

KYIV, May 7 (Reuters) - All women, children and elderly civilians have been evacuated from the Azovstal steel mill in Mariupol, Ukrainian officials said on Saturday, after a week-long effort rescued hundreds of people during an ongoing Russian assault at the plant.

"This part of the Mariupol humanitarian operation is over," Deputy Prime Minister Iryna Vereshchuk wrote on the Telegram messaging app.

The Soviet-era steel mill, the last holdout in Mariupol for Ukrainian forces, has become a symbol of resistance to the Russian effort to capture swathes of eastern and southern Ukraine in the 10-week-old war.

Under heavy bombardment, fighters and civilians have been trapped for weeks in deep bunkers and tunnels criss-crossing the site, with little food, water or medicine.

Russian forces backed by tanks and artillery tried again on Saturday to storm Azovstal, seeking to dislodge the last Ukrainian defenders in the strategic port city on the Azov Sea, Ukraine's military command said.

Weeks of Russian bombardment have left Mariupol in ruins. The steel mill has been largely destroyed. During pauses in fighting, evacuations of civilians began last weekend, brokered by the United Nations and the International Committee of the Red Cross.

Ukrainian President Volodymyr Zelenskiy said in a late night address that more than 300 civilians had been rescued from the plant. Authorities would now focus on evacuating the wounded and medics, and helping residents elsewhere in Mariupol and surrounding settlements to safety, he said.

Russian-backed separatists have also reported a total of 176 civilians evacuated from the plant. It was not clear if civilian men were still there.

Ukrainian fighters in the plant have vowed not to surrender. It was unclear how many remained, and Ukrainian officials fear Russian forces want to wipe them out by Monday, when Moscow commemorates the Soviet Union's victory over Nazi Germany in World War Two.

In Washington, U.S. Central Intelligence Agency Director William Burns said Russian President Vladimir Putin is convinced "doubling down" on the conflict will improve the outcome for Russia.

"He's in a frame of mind in which he doesn't believe he can afford to lose," Burns said at a Financial Times event.