The counter-proposals came after two days of intense talks under mediation of a Spanish cabinet minister who flew to Panama City for emergency meetings aimed at resolving the spat.
The Grupo Unidos por el Canal (GUPC) consortium, led by Spanish builder Sacyr, has threatened to suspend the expansion work by January 20th unless Panama pays for $1.6 billion (€1.17 billion) in "unforeseen" costs.
The Panama Canal Authority proposed the creation of a special $283 million fund to ensure the work continues, but the companies asked for a larger contribution from the Panamanians.
"If they don't accept the proposal and they don't withdraw the work suspension threat, then we would take the next step to terminate the contract, if necessary," canal administrator Jorge Quijano said after two hours of negotiations with the companies.
The two sides may meet again on Wednesday or later this week, Quijano said.
Panamanian officials suggested that each side put up $100 million, while GUPC would have two extra months to pay back an $83 million advance payment.
The consortium agreed to contribute $100 million but it demanded $400 million from the canal authority and asked for the $83 million to be repaid only after the dispute is resolved through arbitration.
In a statement, GUPC said the canal authority's proposal was only a "partial solution."
But it said it was willing to "continue the dialogue to go from a short-term proposal to a long-term one that allows the conclusion of the work."
Already facing delays, the project aims to make the 80-kilometer (50-mile) waterway, which handles five percent of global maritime trade, big enough to handle new cargo ships that can carry 12,000 containers.
The project is costing $5.2 billion, including a $3.2 billion contract for GUPC to build a third set of locks for the century-old canal, which currently welcomes ships that carry up to 5,000 containers.
The negotiations opened on Tuesday after Spanish Public Works Minister Ana Pastor held separate meetings a day earlier with Panamanian President Ricardo Martinelli, company executives and canal officials.
GUPC, which includes Impreglio of Italy, Belgium's Jan de Nul and Constructora Urbana of Panama, agreed to negotiate with the canal authority within the contract.
Sacyr shares bounced back during the negotiations, closing 4.72 percent higher in Madrid after tumbling when the crisis erupted last week.
The work began in 2009 and was supposed to conclude this year, but it is nine months behind schedule and is now expected to be finished in June 2015.
GUPC says it ran into unforeseen costs because the canal authority gave the builders the wrong information regarding the area's geology.
The canal authority has countered that the contractor's claims "lack any foundation" and that GUPC must make its complaint in the legal bodies outlined in the contract.
The extra funds proposed by canal officials would be used to pay contractors and subcontractors.
Under the offer, GUPC would be required to deliver next month four canal lock-doors that were supposed to arrive last November and have already been paid for.
The canal authority says it has paid almost two thirds of its contract with GUPC.
Spain is a major player in global infrastructure projects. In 2011, a Spanish consortium won a €6.7-billion contract to build and operate a 450-kilometre (280-mile) high-speed rail link in the desert between the holy cities of Mecca and Medina.
Spain's first big foreign rail contract was signed with Turkey. A Spanish consortium built the high-speed rail link between Ankara and Istanbul which was inaugurated in 2009.
Spain's airports authority AENA is the largest in the world and operates 46 airports in Spain alone.