Updated

Republicans on Capitol Hill Tuesday voiced frustration over President Obama’s handling of the crisis in Ukraine, criticizing his second round of sanctions against those in Russian President Vladimir Putin’s inner circle as too weak.

“Clearly, more steps must be taken to put pressure on Russia, and it is past time we reassess our entire strategy towards a nation that poses an increasing threat to international peace and security,” House Majority Leader Eric Cantor said in a written statement Tuesday.

Cantor’s comments came on the same day Putin signed a treaty in Moscow making Crimea again part of Russia despite Ukrainian protests and threats of Western sanctions.

Cantor says while he supports Obama’s decision to issue more sanctions, the list falls short and must be “dramatically expanded to exert real pressure.”

One way would be to revoke Russia’s membership in the G-8, Cantor said.

He also believes the United States should assess the military support it can provide Ukraine and should also “work in concert with its NATO allies to reassure other countries threatened by Russia.”

“We should also assess what support we can give to Ukraine's energy production and to increase our own exports to weaken Russia's stranglehold, and put long-term pressure on their economy,” Cantor said. “I've asked House Committees to examine additional steps that can be taken to impose greater costs on Russia, and look forward to working with President Obama and his Administration to confront the brazen challenge to international security posed by President Putin's aggression."

Tennessee Republican Sen. Bob Corker also wants Obama to step up the severity of the sanctions.

“The president’s announcement of additional sanctions against Russia represents a step in the right direction, but won't do enough to modify Russian behavior,” Corker said in a written statement. “‎So far, the administration’s calibrated actions have failed to affect Vladimir Putin’s decisions, and that has to change.”

In Washington, White House spokeswoman Caitlin Hayden said Obama wants to gather world leaders from the G-7 ahead of next week’s global meeting in the Netherlands to discuss the escalating situation.

Russia is one of 53 countries which will participate in the meeting in The Hague.

In a statement, Hayden said the meeting that Obama is organizing "will focus on the situation in Ukraine and further steps that the G-7 may take to respond to developments and to support Ukraine."

The G-7 includes the United States, Britain, Germany, Japan, France, Italy and Canada. Russia joined to form the G-8 in the 1990s, but has been a bit of an odd man out at their annual meetings. The G-8 has been eclipsed in recent years by the G-20, which includes China and emerging markets and was created to better represent the drivers of the 21st century global economy.

Russia has the G-8's rotating leadership and is scheduled to host a summit in Sochi in June, but the other members already have suspended preparations for that meeting over objections to Russia's involvement in Ukraine.

On Monday, Obama sanctioned seven high-ranking Russian officials. The administration also announced sanctions against separatist leaders in Crimea and former president of Ukraine Viktor Yanukovych.

The expanded U.S. sanctions, announced in an executive order, target the assets of the listed Russian officials and bars them from entering the U.S. These include Putin aides Vladislav Surkov and Sergey Glazyev.

"The crisis in Ukraine calls for a far more significant response from the United States. Today's Executive Order could be an important part of that response, but sanctioning only seven Russian officials is wholly inadequate at this stage," Sen. John McCain, R-Ariz., said in a statement Monday.

McCain also took to Twitter to urge military aid for Ukraine.

The Associated Press contributed to this report.