The construction group has threatened to halt the massive project within three weeks if the Panama Canal Authority fails to pay for the extra costs.
But President Ricardo Martinelli said he expected the Grupo Unidos por el Canal (GUPC) consortium to finish the work "without any setbacks, because these cost overruns are irresponsible".
"I will go to Spain and Italy to demand these governments take moral responsibility for what happened, because it is not possible that a company put huge extra charges on expansion work," he said.
Martinelli did not put a date on his trip.
In a letter to canal authorities dated December 30, Spanish builder Sacyr, the consortium's leader, gave a 21-day deadline before suspending its $3.2 billion contract (€2.3 billion) to expand the capacity of the canal, notably by installing a third set of canal locks.
The project aims to make the 80-kilometre (50-mile) waterway, which handles five percent of global maritime trade, big enough to handle new, mega cargo ships that carry 12,000 containers.
"GUPC has formally informed the Panama Canal Authority that it will suspend work if the failures to comply are not put right within the advised period," Sacyr told Spanish market regulators.
The overall cost of the project has been estimated at $5.2 billion.
News of the suspension threat sent Sacyr shares plunging by more than 18 percent as trade opened on the Madrid stock exchange. They ended the day down 8.95 percent at €3.43.
The consortium also includes Impregilo of Italy, Belgian firm Jan De Nul and Panama's Constructora Urbana.
On Wednesday, Panama canal administrator Jorge Quijano warned that the canal authority would use contractual mechanisms to ensure the completion of the canal expansion.
His predecessor, Alberto Aleman, who was in charge when the work began, said Sacyr has underestimated Panama's ability to fend off the group's demands.
"Panama is in a position to finish the work and the country will handle this very well," he said.
A year ago, GUPC demanded an extra payment of $1.6 billion from the Panama Canal Authority due to construction delays.
"There are many and varied unforeseen costs which came up during these gigantic works," a Sacyr spokesman told news agency AFP.
"They are technical matters, questions over cement ingredients, geotechnical matters, geological questions, taxes matters, financial matters, labour issues and weather conditions," he said.
The group began work on a third set of locks for the canal in 2009 and expects to complete construction in June 2015, already a nine-month delay over the date set in the contract.
The new locks will accommodate larger ships with more than double the maximum capacity of 5,000 containers of those that are now able to navigate the canal.
Between 13,000 and 14,000 ships navigate the canal each year and more than one million have crossed it in the past 100 years.
According to the canal authority, there was a delay of four months shortly after the project began to reverse a GUPC plan to use lower-quality cement.
But Sacyr said the cost overruns were due to "unforeseeable" circumstances and had been reported to the relevant authorities, including the Dispute Adjudication Board.
"GUPC is maintaining communication with the Panama Canal Authority to reach a satisfactory agreement to put an end to the contractual imbalance," it added.
The canal uses a system of locks that raises ships from sea level and carries them through the continental divide.