Zebari said his country was making major progress in finalising the deal by the end of June and the US was showing "great flexibility".
The presence of tens of thousands of foreign private security contractors in Iraq has been heavily criticised, especially after the killing last year of 17 Iraqis in Baghdad by Blackwater, a US company which protects American officials in the country.
The US and Iraq are negotiating a new agreement to provide a legal basis for US troops to stay in Iraq after December 31, when their UN mandate expires.
However the Status of Forces Agreement (Sofa) has caused controversy and angry protests in Iraq after media reports said the US was demanding immunity for contractors.
There were also reports - denied by US officials - that the deal provided for the presence of up to 50 permanent military bases in the nation.
Zebari's comments contrast with remarks last week by Nuri al-Maliki, the Iraqi prime minister, who said that talks with the US on the new long-term security pact had reached a "dead end" as the US had made demands that "hugely infringe" on Iraq.
However, David Satterfield, the US state department's senior adviser on Iraq, said last week that negotiations on the agreement were on schedule.
No 'offensive actions'
Zebari said the new agreement would also state that Iraq cannot be used for "any offensive actions" against "any" of Iraq's neighbouring countries, in reference to ongoing US tensions with Iran over its nuclear programme.
However, the US would be granted control of Iraqi airspace below about 9,700m, he said.
He added that the deal would not be binding for the next US president following elections in November, and that any new administration would have the right to review or terminate the agreement as it saw fit.
And the Iraqi foreign minister said he had spoken to Barack Obama, the US Democratic presidential candidate, who had assured him that, if elected, he would make "no reckless or drastic" decision to withdraw US troops from Iraq.
"Any decision for a timetable would be made through close consultation," he said.