U.S. and European stocks ticked higher on Tuesday as a sell-off in bonds moderated, although investors remained cautious ahead of U.S. consumer price inflation data on Wednesday and Donald Trump's inauguration as president next week.

Stocks and bonds declined in response to much better-than-expected job growth. This week's CPI report could further pressure yields.

Stock markets mostly rose Tuesday with traders' attention fixed on President-elect Donald Trump's tariff plans, earnings updates and upcoming inflation data.

European stocks and U.S. futures rose on Tuesday as a sell-off in bond markets moderated, although investors remained cautious ahead of U.S. inflation data on Wednesday and the start of U.S. President-elect Donald Trump's second term in office next week.