Four suspects arrested in the Moscow concert hall attack that killed more than 130 people appeared in court on terrorism charges Sunday, Russian state media reported.

The big picture: An ISIS affiliate claimed responsibility for one of Europe's deadliest terrorist attacks, which Russian leader Vladimir Putin sought to tie to Ukraine as he declared Sunday a national day of mourning for the Crocus City Hall shooting victims.

• U.S. officials have also asserted that the Afghanistan-based ISIS-K, a regional branch of ISIS that's active in South-Central Asian countries including in Tajikistan, was behind the attack that analysts say poses a threat to Putin's strongman image.

State of play: Flags were lowered to half-staff Sunday, as Russian officials announced the death toll from the attack by four gunmen had risen to 137 and said the number of those injured was 182.

• The conditions of some of the more than 100 people being treated in local hospitals were listed as serious.
• Meanwhile, a Moscow court remanded all four attack suspects in custody until May 22, per the state-run Tass news agency.

Zoom in: Suspects Saidakrami Murodalii Rachabalizoda, Dalerdjon Barotovich Mirzoyev and Shamsidin Fariduni, all pleaded guilty during Sunday's pretrial detention hearings, according to state media.

• A fourth suspect, Muhammadsobir Fayzov, was brought into court in a wheelchair and struggled to speak during his appearance, Tass reports.
• All four suspects were identified as being from Tajikistan and all appeared to have injuries during their court appearances.

What they're saying: Putin in a televised address on Saturday announcing the detention of 11 people over the attack did not mention ISIS-K.

• "They tried to hide and moved toward Ukraine, where, according to preliminary data, a window was prepared for them on the Ukrainian side to cross the state border," Putin said of the gunmen.
• Ukrainian officials deny any involvement in the attack and their President Volodymyr Zelensky in a televised addressed said Putin was trying to "shift the blame" onto Kyiv.

Zoom out: The attack came days after Putin claimed victory in an election solidifying his rule throughout the remainder of this decade, which was denounced by the U.S. and other nations as neither free nor fair.

• Just before the election, the U.S. Embassy in Moscow said it was monitoring reports of "imminent" extremist plans to target large gatherings in the Russian capital, including at concerts.
• Russian intelligence officials announced around this time that they had prevented a terrorist attack on a Moscow synagogue.
• Despite this, Putin said on March 19 that statements by Western officials "about the possibility of terrorist attacks in Russia" resembled "outright blackmail and an intention to intimidate and destabilize our society," Tass reported.

Between the lines: As Russia faces the threat of extremism at home, Putin is facing a costly war in Ukraine.

• RAND research analysis estimates that direct military spending for Russia's invading forces "may amount to $132 billion through 2024."
• Mark Galeotti, a Russia analyst at University College London, said Russian intelligence agency the FSB's main resources had been focused on Ukraine and "the domestic opposition," per The Guardian.
• "The FSB obviously had their priorities wrong," he said. "These are the priorities placed upon them from the top."

Editor's note: This article has been updated with new details throughout.