The meeting signalled a "desire for continued engagement at high levels between the two countries", said an external affairs ministry statement.
The visiting Omani foreign minister congratulated Sushma Swaraj on her assumption of office and hoped to further consolidate the strong bilateral relations between the two countries.
Both took stock of various aspects of bilateral relations, including political, economic, defence, security and people-to-people linkages, and agreed to further strengthen them.
Abdullah invited Sushma Swaraj to visit Oman at an early date, to which she agreed. Dates would be decided through diplomatic channels, the statement said.
The two leaders also discussed enhancing project exports from India to Oman.
In 2013, Indian companies bagged contracts worth $1.25 billion in Oman.
Both the ministers felt this trend should be continued. They agreed to convene the India-Oman Joint Commission at an early date during the year so as to provide further impetus to the growing economic and commercial engagement.
The two sides also discussed the welfare of the large Indian community in Oman, numbering more than 700,000.
Abdullah is the first foreign dignitary to visit India after the new government assumed office in New Delhi.
Bilateral trade between Oman and India is worth $5 billion per annum, which is likely to increase to $6 billion in the next financial year.
There are over 50 India-Oman joint ventures in the Gulf country.
India and Oman also engage in defence cooperation with naval exercise Naseem-Al-Bahr (Sea Breeze) and air exercise Al Jisr Al Sharqi (Eastern Bridge).
The two countries are also cooperating in anti-piracy operations in the Gulf of Aden.
Remittances from Oman to India are annually estimated at $3 billion.