Gabriel, who is also Germany's Economy Minister, said that a Greek letter sent to lenders Thursday seeking a six-month loan extension was insufficient but added that the key question was what reforms Athen's new government was willing to undertake.
Earlier, German Finance Ministry spokesman Martin Jäger had said Thursday's Greek proposal to lenders, including the EU and International Monetary Fund, to extend bailout dates and terms was "not a proposal that leads to a substantial solution."
Gabriel and Schäuble are ministers in the grand coalition cabinet of Chancellor Angela Merkel, which has consistently insisted that Greece make extensive reforms stipulated in past bailout agreements.
The European loan program to Greece expires at the end of this month.
First step, says source
A source close to Gabriel, who is also leader of Germany's Social Democratic Party (SPD), quoted by the German press agency DPA, said the Greek letter was a "first step in the right direction."
Gabriel believed that Greece should not be publicly rejected "in advance," the source told DPA.
Further eurozone talks on Friday
Eurogroup head Jeroen Dijsselbloem of the Netherlands and other finance ministers of the 19-member eurozone are due to meet in Brussels on Friday to consider Greece's proposal to extend the loan program.
Friday's meeting will be the third in little over a week since signs of compromise emerged after previous talks ended in recrimination.
A top European official quoted by the news agency AFP said the stand-off had come down to a clash of personalities between Schäuble, the euro's powerful defender, and Greece's new finance minister Yanis Varoufakis.
Greece claims that its request satisfies the demands of its lending partners, while also keeping a promise to end austerity conditions detested by many Greeks.
France's Valls optimistic
French Prime Minister Manuel Valls said on Thursday he believed that Greece's six-month extension request showed that the stand-off could be solved "very quickly."
Valls said he took recent declarations by Greece's new leftist prime minister, Alexis Tsipras, as a "very encouraging sign" that a prompt solution was possible.
France would keep pushing for Greece to "keep its place in Europe, which welcomed it when it left dictatorship," said Valls, referring to 1974.
Greece's deep recession has left nearly one-third of the population living at or below the poverty line and 26 percent of Greeks unemployed.
ipj/kms (AFP, Reuters, dpa, AP)