Heritage bosses hope the cash can be found to enable the Eastney attraction to move into a Centre for Discovery in Portsmouth Historic Dockyard.
The project has already been given a huge boost after the Heritage Lottery Fund pumped £13.85m into the plans. But another £2.5m is still needed.
Efforts got under way at the Great South Run when runners raised nearly £1,500 for the cause.
Meanwhile, a consultation is ongoing over proposals to move the iconic Yomper statue to the dockyard.
John Rawlinson, director of visitor experience at the National Museum of the Royal Navy, said: ‘We’re absolutely delighted that our Great South Run museum team raised an incredible amount of money for our appeal. A huge part of the appeal is to relocate the Royal Marines Museum to Portsmouth Historic Dockyard, so we can tell the Royal Marines’ rich history to more people.
‘It was especially important to have 12 Royal Marines running for our team.
‘Activity is going to be right at the heart of the new museum.
‘We’ve already had some excellent news in securing funding from the Heritage Lottery Fund, and the Great South Run fundraising was the launch of our campaign towards reaching the total target of £2.5m for the appeal.’
The appeal will also allow the museum to create new galleries, offer hands-on activities and reveal personal stories of heroism.
Should the project go ahead, more than two million artefacts would be relocated.
Many of the items, which include everything from rare documents, photographs, medals, paintings and archaeology, are currently at risk in buildings and stores ‘not fit for purpose’ say museum bosses.
People can still donate money to the Great South Run team at justgiving.com/fundraising/gsrfornmrnTo stay up to date on the museum’s fundraising, visit: nmrn.org.uk/get-involved/fundraising-blogA petition calling for the Yomper statue to stay at its home in Eastney has now attracted more than 2,000 signatures.
Campaigners have taken a stand against the re-location of the Falklands memorial as it’s a powerful reminder of the area where marines trained – and the sacrifices made by so many. Members of Portsmouth City Council also unanimously backed the calls.