Its report recommends increasing funding and improving links between UK and Scottish programmes.
The Carbon Trust recently said marine power could create 10,000 jobs by 2020.
By 2050, it said, the global market could be worth £340bn, with the UK claiming about one-fifth of the business.
And with the UK possessing seven out of the eight large-scale prototypes deployed anywhere in the world, it was well-placed to lead the global race, the MPs said.
"In the 1980s the UK squandered the lead it had in wind power development, and now Denmark has a large share of the worldwide market in turbine manufacturing," said Tim Yeo MP, the committee’s chairman.
"It should be a priority for the government to ensure that the UK remains at the cutting edge of developments in this technology and does not allow our lead to slip."
The committee’s report, The Future of Marine Renewables in the UK, included an examination of tidal stream generators, where devices such as big rotors are turned by the incoming and outgoing tides, but excluded barrage technologies such as the mooted Severn Barrage, which tend to be much more expensive and can cause big ecological problems.
It has been estimated that wave and tidal technologies could supply about one-fifth of the UK’s current electricity demand, and many other nations are becoming interested, in particular the Nordic countries, South Korea and China.
But currently they are expensive – about five times the price of onshore wind, for example.
As with other new technologies, the government expects costs to fall dramatically once devices and installation become standardised.
La Rance tidal barrage La Rance barrage, opened in 1966, was until recently the world’s biggest tidal power facility
But there is little chance of marine power making a major contribution by 2020.
The government recently reduced its estimate of the 2020 contribution from 1-2 gigawatts (GW) to 200-300 MW, and the committee says that should be looked at again, as several industry experts have said the new target can be met easily.
The size of the UK funding pot for marine renewables, at £20m, should also be re-examined, they say. And deployment of that money should be co-ordinated better with the Scottish government, which has a separate £18m budget.
The level of subsidy companies receive up to 2017 is secure, the MPs say – but longer-term clarity is needed in order to give investors confidence.
David Clarke, chief executive of the Energy Technologies Institute, a government-industry collaboration, said time was of the essence.
"The marine renewables industry must demonstrate its ability to be cost-competitive, compared with other low-carbon technologies, in the next 5-8 years if it is to engage commercial investors," he said.
"If it doesn’t, other technologies will be built as alternatives; investors will feel more assurance in them and see more opportunity for return."
With projects such as Marine Current Turbines’ tidal generator in Strangford Lough showing the technologies can work with no discernible impact on local ecology, the next step will be to build arrays of several connected devices; but each array would cost around £40-50m, the committee heard, meaning current levels of support could be inadequate.
Another recommendation from the committee is that with many of the best sites in remote locations around northern and western Scotland and in the Orkneys and Shetlands, finance for grid connection needs ramping up.
Environment groups who have long bemoaned the slow pace of development on wave and tidal power endorsed the committee’s recommendations.
"This report is a great reminder of the massive potential of marine renewables in the UK," said Nick Molho, head of energy policy at WWF-UK.
"Investment certainty holds the key to reducing the costs of marine renewable and creating jobs; the government would be mad to miss this boat."
A spokeswoman for the Department of Energy and Climate Change said the government welcomed the report and was studying its recommendations.
"We are fully committed to spurring on the growth of this industry and have already taken great strides to make this happen," she said.