MEND lauded the decision of the House to invite Jonathan, but said if the ex-President refuses, the lower chamber should mandate him.
Razak Atunwa, the Chairman of the House ad-hoc panel investigating the contract of Oil Prospecting License (OPL) 245 had said the committee will invite Jonathan to shed light into the Malabu deal.
The ex-president allegedly received $200 million kickback from the deal, but he denied the claim.
In a statement issued by MEND spokesman, Jomo Gbomo, the group urged the House to mandate Jonathan's appearance.
The statement said: "We are compelled by natural justice, equity and good conscience to lend our voice to the most ignoble and despicable role played by the former President in the messy affair which has tainted the image of Nigeria, both locally and internationally.
"Like millions of Nigerians at home and in the Diaspora, who have keenly followed the OPL 245 saga, we have reasonable grounds to suspect that former President Jonathan may have indeed compromised his high office with regard to the matter, more especially, given the fact that key officials of his administration, including the then Attorney-General of the Federation, Mr. Mohammed Bello Adoke, have been indicted and charged before the Federal High Court in Abuja.
"We are in full support of moves by the House of Representatives to summon the former President to appear before the House to give answers to the myriad of questions concerning his role in OPL 245 saga.
"Where he (Jonathan) refuses to honour the invitation, we urge the House to invoke its inherent powers to compel his appearance."
MEND also expressed shock at the media reports of the planned relocation of Shell Petroleum Development Company of Nigeria Limited (SPDC) to Lagos from Port Harcourt, Rivers State.
It added, "Besides the massive loss of jobs, opportunities, taxes and other incentives, the planned move (by SPDC) will cause in the medium to short term, it is clear to all stakeholders, including the Federal Government, that such a move is ill advised, especially against the backdrop of the recent directive from the federal government to the International Oil Companies (IOCs) to relocate to their areas of operation in the Niger Delta.
"To be sure, the Niger Delta region is no longer hostile to the business interests of the IOCs, including SPDC, as peace has since returned to the region; following the enervating efforts of MEND, the Pan-Niger Delta Forum (PANDEF), the various state governments and the federal government. There is therefore no reason whatsoever for SPDC to relocate to Lagos."
The militant group threatened to end the unilateral ceasefire of May 30, 2014, if SPDC relocates to Lagos.