The negotiations began after Compromis, a small, regional grouping involved in coalition talks, submitted a last-ditch proposal for a government which is currently being examined by other parties.
"We think there is still time and we have to try this," Hernando told reporters more than 18 weeks after inconclusive December elections resulted in a hung parliament and forced parties into coalition talks that have so far failed.
The proposal came as King Felipe VI prepared to wrap up consultations with various party leaders before issuing a statement later Tuesday or Wednesday expected to make clear whether there was any hope for a coalition deal, or whether fresh elections were inevitable.
Until the restart of talks on Tuesday, all bets had been on new polls, which would be held on June 26 under an official electoral timeframe.
This would mean Spaniards would cast their ballot again just six months after December's elections, which put an end to the country's traditional two-party system in a historic result as voters flocked to new groupings.
But the election left Spain in uncharted waters as the country has never had a coalition government since it returned to democracy following the death of long-time dictator Francisco Franco in 1975.