ZURICH, Jan 29 (Reuters) - The Swiss National Bank has agreed a new deal with the Swiss government which could see the central bank increase its annual payments to Bern and the country's local governments to 6 billion Swiss francs ($6.7 billion).

The new profit distribution agreement covers the financial years from 2020 to 2025. Under the previous arrangement, the SNB could make a maximum payout of 4 billion francs.

The SNB has faced calls from some politicians in recent weeks to help support the economy, which has been hit hard by the COVID-19 downturn and lockdowns introduced to tackle the virus.

The increased payment will be made "if the SNB's financial situation permits", the central bank said on Friday. The full payout will be made if the SNB makes a profit of 40 billion francs.

The SNB said earlier this month it expected to make a profit of around 21 billion francs for 2020 as soaring gold and stock markets boosted the value of its foreign currency assets.

After taking into account the bank's distribution reserves, its 2020 net profit will be in the region of 98 billion francs, meaning it will make the full 6 billion franc payout for 2020.

The SNB makes a profit from its vast holdings of foreign currency investments built up during its long campaign to slow the rise of the safe-haven Swiss franc.

The bank currently holds 910 billion francs worth of foreign currency assets, including stakes in companies like Tesla and Apple. ($1 = 0.8902 Swiss francs) (Reporting by John Revill; Editing by Louise Heavens and Alison Williams)