Mr Hague was speaking after a two-day visit to Israel and the Palestinian territories, where he urged both sides to return to direct talks which were suspended over the issue of Israeli settlements on the West Bank.
The Foreign Secretary warned that if the two-state option failed, the world could face problems in the Middle East for "much, much longer into the future".
Since the 1990s, the idea of a two-state solution with a sovereign Palestine existing alongside a secure Israel has been an increasingly dominant theme of efforts to bring about an end to conflict in the Middle East.
US President George Bush's declaration of support for a two-state solution in 2002 cleared the way for its inclusion in United Nations Security Council Resolution 1397 and it was enshrined that year in the "road map" for peace backed by the Quartet of the US, EU, UN and Russia.
However slow progress in talks, coupled with the domination of Gaza by the Hamas movement and the continued construction of Israeli settlements in the West Bank, has led to growing uncertainty over whether the goal is attainable.
Mr Hague told BBC1's Andrew Marr Show: "We have to persist, but my concern is that the window is closing on finding a two-state solution in the Middle East.
"If we don't succeed in that soon, then we may be left with this problem for much, much longer in the future."
Mr Hague said Israeli Prime Minister Benjamin Netanyahu "says he wants to get back into these talks with the Palestinians, that he largely can see the way to a settlement of this, but it will remain a phenomenally difficult issue".
The Foreign Secretary is due to visit Washington in two weeks' time for talks with US Secretary of State Hillary Clinton on how to take the process forward.
"It is only the US that can deliver Israel to a negotiated agreement," he said. "It is the US that has that leverage, but Britain is highly active on this process."
He confirmed Government plans to change the application of the law on universal jurisdiction, which has been used by pro-Palestinian campaigners to threaten Israeli politicians with arrest for war crimes if they enter the UK.