Secretary of State John Kerry is meeting with his Russian counterpart Sergey Lavrov in hopes of de-escalating the standoff, but the chances for a diplomatic resolution appeared slim.
Obama, though, publicly held out hope for a deal and said the two were still meeting.
“We continued to hope for a diplomatic outcome,” the president said.
The pro-Russian government in Crimea will hold a referendum on leaving Ukraine and joining Russia on Sunday.
Russian military forces seized control of the region after Moscow-backed former Ukrainian President Viktor Yanukovych was removed from power.
Russian President Vladimir Putin has rejected calls from Obama and other world leaders to pull back military forces, block the referendum and allow international observers.
The U.S. and European Union have instituted targeted sanctions against individuals deemed to be violating Ukraine's territorial integrity or democracy.
In his meeting with Kenny, Obama praised Ireland as a strong ally and thanked Dublin for its support over Crimea.
“Ireland has been a strong vote in the European Council,” Obama said.