The defending champion, Roglič (Jumbo-Visma) currently leads the overall standings by 28 seconds over his closest rival of Enric Mas of Movistar with the Spaniard's team-mate, Miguel Ángel López in third at 1-21.
Meanwhile, Ineos Grenadiers hold fifth and sixth spots in the general classification, with Egan Bernal and Adam Yates sat either side of the two minute mark after the first week.
Both teams have come out and said they have plans to beat Roglič, but the Slovenian star seems unfazed by this.
Speaking to Spanish paper, Marca, Roglič said: "They [Movistar and Ineos] have two cards to play at the moment. I'm not really frightened, because I have confidence in myself and in my team, but Movistar and Ineos have strong teams and we cannot make any errors,
"Having two such strong riders up there allows them to come up with strategies that could put us in difficulty. We know the strength of those teams, but if my team-mates are going well, we can face up to them as we have on other occasions."
He added that he is very pleased with how everything has gone so far with the two-time Vuelta winning describing his first week as "encouraging".
Mas, Roglič's closest rival and only rider inside a minute, looked very strong on the Alto de Velefique as he managed to attack clear with the leader of the race.
Roglič added he was impressed with Mas' performance, calling him is main rival but he did add that there is a long way to go and other riders can improve and cause him problems.
His final point was: "I believe this second week is going to be more controllable - There are short days, where I go well, and also some opportunities for the sprinters.
"But, as I said, I have to be alert at all times, and the weekend will bring difficult mountain stages, so I'm expecting a hard race."
Thank you for reading 20 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1