(Adds G7 meeting, Yellen, recasts)
* Fate of Azovstal defenders still unclear
* Pro-Russian separatist leader says half have surrendered
By Natalia Zinets and Jonathan Landay
KYIV/SLATYNE, Ukraine, May 19 (Reuters) - The Group of Seven agreed on Thursday to provide Ukraine with $18.4 billion to pay its bills, funds that Ukraine's Prime Minister Denys Shmyhal said would speed up Kyiv's victory over Russia and which were just as important as "the weapons you provide".
U.S. Treasury Secretary Janet Yellen told reporters at the G7 finance leaders' meeting in Germany: "The message was, 'We stand behind Ukraine. We're going to pull together with the resources that they need to get through this.'"
Earlier on Thursday Shmyhal had written on Twitter, "Support of partners will speed up our victory... Despite Russia's efforts to destroy our economy, together we will win!"
Further pledges of weapons also came on Thursday, as U.S. Secretary of State Antony Blinken said on Thursday he has authorized $100 million in additional U.S. arms, equipment, and supplies for Ukraine.
The past week has seen Russia secure its biggest victory since the invasion began, with Kyiv announcing it had ordered its garrison in a steelworks in Mariupol to stand down, after a nearly three-month siege of the city.
Russian forces have lost ground elsewhere, however, driven from northern Ukraine and the area around the capital at the end of March, and pushed this month from the outskirts of the second-largest city Kharkiv.
In Washington, U.S. President Joe Biden on Thursday threw his support behind Sweden and Finland's bids to join NATO in the wake of Russia's invasion of Ukraine.
Finland and Sweden's move reverses generations of military non-alignment and is the biggest shake-up in European security for decades.
NATO member Turkey has objected, accusing the two Nordic states of harbouring Kurdish militants, but Biden and European leaders said they were confident Turkey's concerns could be addressed.
Biden, hosting Swedish Prime Minister Magdalena Andersson and Finnish President Sauli Niinistö at the White House, told reporters: "I think we're going to be OK".
Turkey's President Tayyip Erdogan said late on Wednesday, "We have told allies that we will say no to Finland and Sweden's NATO membership," adding, "NATO is a security alliance and we cannot accept terrorists to be in it."
Niinisto said Finland would commit to Turkey's security, adding, "We condemn terrorism in all its forms and we are actively engaged in combating it."
The ultimate outcome of the bloodiest battle in Europe for decades has remained unclear, with no confirmation of the fate of hundreds of Ukrainian defenders. Moscow said on Thursday that 1,730 Ukrainian fighters had surrendered so far, including 771 in the past 24 hours.
Ukraine, which says it aims to secure a prisoner swap, has not said how many were inside the plant or commented on the fate of the rest since confirming that just over 250 had surrendered in the initial hours after it ordered them to yield.
The Switzerland-based International Committee of the Red Cross said it has registered hundreds of prisoners from the plant now held by Russia, but it has not given a precise number.
The leader of Russian-backed separatists in control of the area said nearly half of the fighters remained inside the steelworks, where underground bunkers and tunnels had protected them from weeks of Russian bombardment.
"More than half have laid down their arms," Denis Pushilin told the Solovyov Live internet television channel. "Let them surrender, let them live, let them honestly face the charges for all their crimes."
The wounded were given medical treatment while those who were fit were taken to a penal colony and were being treated well, he said. Ukrainian officials say they cannot comment publicly on their fate while negotiations are under way to rescue them.
Russia denies it agreed to a prisoner swap. Many of the Azovstal defenders belong to a Ukrainian unit with far-right origins, the Azov Regiment, which Moscow calls Nazis and says must be prosecuted for crimes.
Oleksiy Gromov, Deputy Chief of the Main Operational Department of the General Staff of Ukraine's Armed Forces, told an online briefing that Ukraine had recaptured 23 settlements near Kharkiv in the last two weeks.
On Thursday, the crash of artillery duels resounded across sunlit fields and woodlands north of Kharkiv near the village Slatyne.
Ukrainian troops said fighting was under way around the nearby village of Demetiivka, which the Ukrainian military said was recaptured the previous day, about 8 km from the Russian border.
But Russia is still pressing its main offensive using massed artillery and armour, trying to capture more territory in the eastern Donbas, comprised of the Donetsk and Luhansk regions, which Moscow claims on behalf of separatists.
Ukraine's general staff said Russia's attacks were focused on Donetsk. Russian forces "suffered significant losses" around Slovyansk to the north of Donetsk.
(Reporting by Natalia Zinets and Max Hunder in Kyiv and a Reuters journalist in Mariupol; Additional reporting by Reuters bureaux; Writing by Peter Graff, Stephen Coates, Alexandra Hudson; Editing by Richard Pullin, Nick Macfie and Hugh Lawson)