William Hague said there remains a "good chance" of a deal being struck soon with Iran over its nuclear programme despite talks between foreign ministers ending without agreement.
The Foreign Secretary said a pact with Tehran "is on the table and it can be done" after good progress was made on narrowing the gaps between Western nations and Tehran.
Optimism about a potential breakthrough in the decade-long dispute was raised when senior politicians including US secretary of state John Kerry flew to Geneva for face-to-face talks.
But with France believed to be holding out for tougher conditions to be placed on Iran in return for the possible lifting of some sanctions, a final late-night two-hour session broke up without accord.
National negotiators will reconvene in the Swiss city on November 20 and Mr Hague said it was "vital to keep the momentum" created over recent days.
Asked if a deal could be done this month, he told BBC1's Andrew Marr Show: "There is a good chance of that but it is a formidably difficult negotiation.
"I can't say exactly when it will conclude but...our negotiators will be trying again so we will keep an enormous amount of energy and persistence behind solving this."
The remaining gaps between the two sides were "narrow", he said.
"These talks have been very detailed. They have made a lot of progress and there is no doubt...that the parties are closer together than before we had these talks.
"There are still some gaps. They are narrow gaps.
"So we haven't been wasting our time but it is a formidably difficult negotiation of course and we are going to reconvene these talks in 10 days' time here in Geneva and try to maintain that momentum.
"It is vital to keep the momentum. There is a deal there. A deal is on the table and it can be done."
Mr Hague said there was "bound to be a terrible lack of trust" of Tehran given its history of hiding its nuclear programme but he said he believed Iranian foreign minister Mohammad Javad Zarif had been "very constructive" and was "out to do a deal".
He insisted that the six-nation E3+3 group negotiating with Iran - the US, Russia, China, Britain, France, and Germany - had been "clearly united" at the end of the talks.
"We were all saying the same thing to Iran and supporting the same deal that can be done and that is something for the Iranians to think about over the next few days."
Mr Hague also cautioned Israel that compromises would be needed to secure a deal - after strong criticism of the putative agreement was expressed by prime minister Benjamin Netanyahu.
David Cameron last night joined efforts to reassure Tel Aviv over the discussions, telephoning Mr Netanyahu to discuss the latest developments.
US president Barack Obama has also called the Israeli leader, assuring him of America's continued commitment to preventing Iran from obtaining a nuclear weapon.
The Foreign Secretary said he had spoken to his counterparts.
"Will that be a deal that will please everybody? Well no it won't because compromises will have to be made," he said.
"It is in the interests of the whole world, including Israel...for us to reach a diplomatic agreement that we can be confident in on this issue that otherwise threatens the world with nuclear proliferation and conflict."
Tehran has always insisted its programme is for energy and other civil purposes - not the pursuit of a nuclear weapon capability as suspected by the West.
Mr Zarif said the talks had been " very productive.
"It is something we can build on and move forward," he said.
Mr Kerry hailed " significant progress in working through the approaches to this question of how one reins in a programme that guarantees its peaceful nature.
"There is no question in my mind that we are closer now, as we leave Geneva, than we were when we came, and that with good work and good faith, over the course of the next weeks we can in fact secure our goal."