* Deutsche Bank to boost capital to narrow gap to peers
* Seeks 2.8 bln eur from cap hike, and a further 2 bln eur
* Deutsche sees core tier one ratio at 9.5 pct
* Q1 pretax profit 2.4 bln eur vs Rtrs poll avg 1.7 bln
* New shares seen offered at 5-7 pct discount
Deutsche Bank said it will beef up its balance sheet with a 2.8 billion euro ($3.7 billion) capital increase and unveiled forecast-beating first-quarter earnings following a wave of aggressive cost cuts.
Germany's flagship lender said it will also seek an additional 2 billion euros of subordinated capital over the next 12 months as it strives to narrow the gap with better-capitalised peers.
Deutsche Bank is among a slew of European banks currently raising capital, including Russia's second-largest bank VTB , Germany's second largest lender Commerzbank as well as Greek and Spanish banks.
According to a source close to the Deutsche Bank, the lender aims to improve its ability to increase dividend payouts in coming years. Since 2009, Deutsche Bank has kept its dividend stable at 75 cents a share.
New shares will likely be sold at a discount of 5 to 7 percent to Monday's closing price of 32.90 euros, financial market sources said.
The move was welcomed by analysts, as a bigger capital cushion gives banks greater flexibility to pay dividends and pursue acquisitions.
"It's long overdue. The question is whether it will be enough," said Andrew Lim, analyst at Espirito Santo in London.
Deutsche Bank shares closed up 1.7 percent at 32.90 euros.
Following completion of the capital measures, Deutsche Bank expects its core tier one capital ratio to increase to approximately 9.5 percent, from 8.8 percent at the end of 31 March, 2013.
By comparison, rival Barclays has a core tier one ratio of 8.4 percent, Credit Suisse of 8.6 percent, JP Morgan of 8.9 percent and Goldman Sachs of 9 percent.
In January, co-chief executive Anshu Jain said the question over whether Germany's lender needed a capital hike was driven by uncertainty over the likely burden of future bank regulation.
The Federal Reserve Board has demanded that foreign banks operating in the United States hold as much capital as their U.S. counterparts, regardless of how well their overseas parent companies are funded.
Deutsche on Monday posted a pretax profit of 2.4 billion euros ($3.14 billion), beating analyst expectations for 1.7 billion euros, as aggressive cost cuts outpaced a slight drop in revenues at the investment bank.
First-quarter pretax profit rose 28 percent, while revenue increased 2 percent. Non-interest expenses dropped 5 percent.
In March, Deutsche Bank said it expected a "solid" first-quarter across all businesses and later added it sees margins improving as competitors pull back.
In January, Deutsche Bank announced one-off charges of almost $4 billion to adjust the valuations of risky assets in an attempt to shrink its balance sheet. Then in March, the bank said its full-year pretax profit would be cut by another 600 million euros due to a hike in legal provisions.