Spain and Italy will need massive sovereign bailouts within six months, says Sean Egan, Founding Partner and President of Egan-Jones, an independent ratings agency.

Spain recently accepted a $125 billion bailout arranged by eurozone finance ministers to prop up its banking sector, yet yields in Spanish bond markets spiked anew quickly afterward, reflecting market concerns that Spain's overall debt burdens remain high.

Yields on Spanish 10-year bonds climbed to a record high of 6.82 percent this week, not far from the 7 percent threshold that led to bailouts in Greece, Ireland and Portugal.

The yield on Italian 10-year bonds climbed to 6.27 percent.

High government borrowing costs and a need to prop up the banking sector are both telltale signs that a broader government bailout is on the way.

"It makes little sense to separate the banks’ credit quality from the governments’ credit quality because quite often, they support each other and that’s certainly the case in Italy and Spain," Egan tells CNBC.

"We think that Spain will be back at the table, asking for more than the 100 billion euros [$125 billion] that they just asked for, and we think that Italy will also come to the table within the next six months."

Greece, meanwhile, will hold parliamentary elections on June 17, and fears persist enough leftwing politicians will win and reject austerity measures such as tax hikes and wage cuts attached to bailout payments.

Past Greek administrations agreed to rigid austerity measures in exchange for rescue financing.

Rejecting austerity measures could end the flow of bailout money headed for Athens and precipitate a Greek exit from the eurozone, which could roil Spanish, Italian and other markets.

"The idea of the Spanish bailout was to calm the market in case the Greek elections do not turn out as the E.U. would like," says Gary Jenkins, director of Swordfish Research, according to the Associated Press.

"However the end result was to create more volatility and create more concern."