Yes, But the more important US index is the S&P 500 because it has millions of contracts linked to it and is the biggest ETF in the world linked to it. (Nifty for us is like S&P 500 for them and Sensex for us is like Dow Jones for them in importance)
The S&P 500, the DAX, the FTSE, the EUR-USD, the USD-JPY, the AUD-USD, the US 10 year bonds everything point in one direction (away from risk) and that is very rare.
By the way, I get to know the international markets news from DailyFX news on youtube.
Here is yesterdays summary (they cover US & Europe Markets) -
https://www.youtube.com/watch?v=pV7PEIYHc0g
You need to know some economics to understand their news but it is very in depth and I like it.