Yes, public finance by government may lead to increase in money supply in economy. But, if govt borrows money from central bank, less amount of money is left with central bank to lend it to banks and hence less money supply in economy. I am unable to figure it out.
Central banks can create money 'out of nothing'. So for starters there isn't 'less amount' of money left with the central bank. The amount of money at the central bank is 'infinite'. So it's not because the CB lends X amount of money to the government, that the CB has X amount less money to lend to the banks, the supply of money is not constrained... Off course, creating too much money and monetizing debt can have negative consequences for sure (for example hyperinflation in extreme cases), but that's another discussion. See also here for more info about quantitative easing: https://www.youtube.com/watch?v=4TihoBfdCe8 and here: http://www.investopedia.com/terms/q/quantitative-easing.asp
Edit: comment from Energy numbers: strictly speaking government borrowing money from central banks doesn't increase the money supply, it only increases when the government spends the borrowed money.