IBEX 35 
Data last week showed that US consumer prices fell in April, leading markets to price in 50 basis points (bps), or at least two rate cuts this year, but several Fed officials have expressed caution about when rates may be cut.
As a result, traders are betting on an easing of about 46 basis points this year, with only one rate cut in November fully discounted.
The minutes of the Fed's latest policy meeting, to be released on Wednesday, along with comments from several Fed speakers, will be in investors' focus this week.
On the geopolitical front, Brent crude futures extended gains amid political uncertainty in major producing countries following the death of Iranian President Ebrahim Raisi and his foreign minister in a helicopter crash and as Saudi King Salman, 88, awaits treatment for lung inflammation.
"The death of the Iranian president should not provoke internal instability in Iran insofar as the security forces and the military are under the control of the supreme leader, although there will be elections in 50 days to appoint a new president," analysts at Renta 4 said in a note to clients.
"We reiterate our market view: we do not rule out that stock markets may offer better entry points in the coming months," they added at Renta 4.
After touching nearly nine-year highs last week, Spain's selective IBEX 35 stock market index was up 10.90 points, or 0.10%, to 11,338.60 points, at 0705 GMT on Monday, while the FTSE Eurofirst 300 index of large European stocks was up 0.01%.
In the banking sector, Santander was up 0.28%, BBVA was up 0.05%, Caixabank was up 0.37%, Sabadell was up 0.45%, Bankinter was up 0.47% and Unicaja Banco was up 0.30%.
Among the large non-financial stocks, Telefónica gained 0.24%, Inditex advanced 0.05%, Iberdrola lost 0.04%, Cellnex gained 0.06%, and the oil company Repsol rose 1.08%.
(Information by Benjamín Mejías Valencia; edited by Javi West Larrañaga)
