Mike Hanna, Al Jazeera's correspondent reporting from Jerusalem, said the flurry of meetings illustrated the change in Washington's approach to the peace process.
"What has become clear in recent days is that the Obama administration is dealing with the issues differently ... instead of taking things issue-by-issue, bit-by-bit, it is addressing all the issues at the same time," he said.
Mitchell's visit to Syria, his second in as many months, was an attempt to re-engage Damascus, a key regional player.
The country's support for Hamas, the de facto government in the Gaza Strip, and its relations with Iran, could make Syria key to US efforts to kick-start the peace process.
Mitchell met Bashar al-Assad, the Syrian president, for talks before heading to Israel and the occupied Palestinian territories.
In a statement released after his meeting with al-Assad, Mitchell said he had communicated Obama's intention "to facilitate a truly comprehensive Arab-Israeli peace".
"That peace means between Palestinians and Israelis, between Syria and Israel, and between Lebanon and Israel. And of course, ultimately, the full normalisation of relations between Israel and all of the countries in the region," the statement said.
Syria's official SANA news agency quoted the US envoy as describing his talks with al-Assad as "important and positive".
Relations between the US and Syria were strained under the administration of George Bush, the previous US president, but have begun to improve under Obama.
Al Jazeera's Zeina Awad, reporting from Damascus, said: "If you read the Syrian press and you speak to Syrian officials, there is generally a real respect for Barack Obama and a real appreciation for this on going engagement with Syria and with the Syrian regime."
In June, Washington announced its decision to send an ambassador back to Damascus to replace the envoy who it recalled in 2005 after the assassination in Beirut of Rafiq al-Hariri, the former Lebanese prime minister. However, the promised ambassador is yet to arrive.
Al-Hariri's killing was widely blamed on Syria, although Damascus has steadfastly denied any involvement.
The round of US diplomacy with Israel comes amid tensions between the two allies, both over Iran and the Obama administrations firmer line on Israeli settlement building.
A rare public row has erupted between Israel and the US as Washington tries to get Israel to freeze construction in all its West Bank settlements.
Binyamin Netanyahu, Israel's prime minister, said there were "naturally" differences of opinion between Israel and the US, but that the sides were "trying to reach an understanding".
Netanyahu is due to hold separate meetings with all three US officials - Mitchell, Gates and Jones.
For his part, Gates headed to Israel on Sunday for talks that will cover missile defence, Israel's plan to acquire the multinational F-35 fighter jet and efforts to curb Iran's nuclear ambitions.
'Range of issues'
The Reuters news agency quoted a senior US defence official as saying the Israelis were "antsy" about Iran but were not leaning on the Obama administration to halt its effort at expanded diplomatic engagement with Tehran.
|Netanyahu is due to hold separate meetings with all three US officials [AFP]
Last week, Dan Meridor, Israel's intelligence services minister, said that comments from Hillary Clinton, the US secretary of state, suggested Washington was "already resigned" to Iran gaining a nuclear weapon.
Iran has denied that its nuclear programme is aimed at manufacturing a weapon, saying it is purely for civilian purposes.
Meanwhile, security advisor Jones "will lead a delegation to Israel and the West Bank from July 28-30 to discuss the broad range of issues in our relationships with Israel and the Palestinian Authority," a White House official said.
"This trip builds on discussions special envoy Mitchell and Secretary Gates will have a few days earlier."