* Proposes new rules for how to handle future banking crisis
* Calls for "somewhat" higher contribution to emergency funds
* Banking lobby had asked for cap on payments
* Payments could rise by NOK 300 mln-400 mln/year -lobby (Adds quotes, background, share price)
OSLO, June 21 (Reuters) - Norwegian banks should pay more into two emergency funds that guarantee deposits and help to pay for bank restructurings in a crisis, the government said on Wednesday.
The proposals are part of new legislation the government is putting forward to deal with any future banking crisis.
"These contribution requirements are somewhat higher than the current contribution level, but on par with contributions paid in 2010, relative to the size of the banking sector," the Finance Ministry said in a statement.
"In accordance with the directives, the Ministry also proposes that the contributions shall be adjusted in proportion to the risk profile of each institution," it said.
Banking lobby Finance Norway criticised the proposal, estimating it would increase payments by 300 million-400 million Norwegian crowns ($35.15 million-$46.87 million), and arguing instead that payments should be capped at current levels.
The new legislation also includes a so-called bail-in mechanism, allowing regulators to convert debt to equity to help prevent a bank from defaulting on its obligations.
Shares in Norway's biggest bank DNB were 2.3 percent lower at 1238 GMT, underperforming a 0.7 percent fall in European banking shares.
Government statement in English: bit.ly/2tsI8So ($1 = 8.5337 Norwegian crowns) (Reporting by Terje Solsvik. Editing by Ole Petter Skonnord and Jane Merriman)